A Study to Find the Best Dose of Fezolinetant to Treat Hot Flashes in Women Going Through Menopause

Inclusion Criteria: * Subject has a body mass index ≥ 16 kg/m\^2 and ≤ 38 kg/m\^2 at screening visit. * Subject must be seeking treatment or relief for vasomotor symptoms (VMS) associated with menopause and confirmed as menopausal per 1 of the following criteria at the screening visit: For post-menopausal subjects: * Spontaneous amenorrhea for ≥ 12 consecutive months * Spontaneous amenorrhea for ≥ 6 months with biochemical criteria of menopause (follicle-stimulating hormone \[FSH\] \> 40 IU/L); or * Having had bilateral oophorectomy ≥ 6 weeks prior to the screening visit (with or without hysterectomy) For peri-menopausal subjects: * Skipped menstrual period with amenorrhea for ≥ 60 days but \< 6 consecutive months with biochemical criteria of peri-menopause (FSH \> 25 IU/L); or * Spontaneous amenorrhea for ≥ 6 months but \< 12 consecutive months with biochemical criteria of peri-menopause (FSH \> 25 IU/L and ≤ 40 IU/L) * Within the 10 days prior to randomization, subject must have a minimum average of 7 mild, moderate and severe hot flashes (VMS) per day. * Subject is not pregnant and at least 1 of the following conditions apply: * Not a woman of childbearing potential (WOCBP) * WOCBP who agrees to follow the contraceptive guidance from the time of informed consent through at least 21 days after the final study treatment administration * Subject must agree not to breastfeed starting at screening and throughout the study period and for 21 days after the final study treatment administration. * Subject must not donate ova starting at first dose of investigational product (IP) and throughout the study period and for 21 days after the final study treatment administration. * Subject is in good general health as determined on the basis of medical history and general physical examination, including a bimanual clinical pelvic examination and clinical breast examination devoid of relevant clinical findings, performed at the screening visit; hematology and biochemistry parameters, pulse rate and/or blood pressure, and electrocardiogram (ECG) within the reference range for the population studied, or showing no clinically relevant deviations. * Subject has documentation of a normal/negative or no clinically significant abnormal findings on breast imaging (obtained at screening or within the prior 12 months of screening). Appropriate documentation includes a written report or an electronic report indicating normal/negative or no clinically significant abnormal findings on breast imaging. * Subject is willing to undergo a transvaginal ultrasound (TVU) to evaluate the uterus and ovaries at screening and week 12 (end of treatment), and for subjects who are withdrawn from the study prior to completion, a TVU at the early discontinuation visit. This is not required for subjects who have had a partial (supra-cervical) or full hysterectomy. * Subject is willing to undergo endometrial biopsy at any time during the study in the case of uterine bleeding. This is not required for subjects who have had a partial (supra-cervical) or full hysterectomy and for peri-menopausal subjects in case of menstrual bleeding. * Subject has documentation of a normal or not clinically significant abnormal Pap test (or equivalent cervical cytology) within the previous 12 months of screening or at screening. This is not required for subjects who have had a full trachelectomy. * Subject has a negative urine pregnancy test at screening. Urine pregnancy test is not required for female subjects who are assessed as post-menopausal status. * Subject has negative serology panel (i.e. negative hepatitis B surface \[HBs\] antigen) and negative hepatitis C virus \[HCV\] antibody) at screening. * Subject agrees not to participate in another interventional study while participating in the present study. Exclusion Criteria: * Subject uses a prohibited therapy (strong or moderate cytochrome P450 1A2 \[CYP1A2\] inhibitors, hormone replacement therapy \[HRT\], hormonal contraceptive or any treatment for VMS \[prescription, over the counter, or herbal/Chinese medicine\]) or is not willing to wash out and discontinue use of such drugs for the full duration of study conduct or it is not medically appropriate to discontinue such drugs for the duration of the study. * Subject has known substance abuse or alcohol addiction within 6 months of screening. * Subject has a history of a malignant tumor except for non-metastatic basal cell carcinoma of the skin. * Subject has uncontrolled hypertension. * Subject has a history of severe allergy, hypersensitivity, or intolerance to drugs in general, including the IP and any of its excipients. * For subjects with a uterus: Subject has an unacceptable result from the TVU assessment at screening, (i.e., full length of endometrial cavity cannot be visualized or presence of a clinically significant abnormal finding). * Subject has a history of an undiagnosed uterine bleeding within the previous 6 months of screening. * Subject has a history of seizures or other convulsive disorders. * Subject has a medical condition or chronic disease (including history of neurological \[including cognitive\], hepatic, renal, cardiovascular, gastrointestinal, pulmonary \[e.g., moderate asthma\], endocrine, or gynecological disease) or malignancy that could confound interpretation of the study outcome. * Subject has active liver disease, jaundice, or elevated liver aminotransferases (alanine aminotransferase \[ALT\] or aspartate aminotransferase \[AST\]), elevated total or direct bilirubin, elevated international normalized ratio (INR), or elevated alkaline phosphatase (ALP) at screening. Subject with mildly elevated ALT or AST up to \< 1.5 × the upper limit of normal (ULN) can be enrolled if total and direct bilirubin are normal. Subject with mildly elevated ALP (up to \< 1.5 × ULN) can be enrolled if cholestatic liver disease is excluded and no cause other than fatty liver is diagnosed. Subject with Gilbert's syndrome with elevated total bilirubin (TBL) may be enrolled as long as direct bilirubin (DBL), hemoglobin and reticulocytes are normal. * Subject has creatinine \> 1.5 × ULN; or estimated glomerular filtration rate (eGFR) using the Modification of Diet in Renal Disease formula ≤ 59 mL/min/1.73 m\^2 at screening visit. * Subject has a previous positive test for the human immunodeficiency virus. * Subject has a history of suicide attempt or suicidal behavior within the prior to 12 months of study enrollment or has suicidal ideation within the prior to 12 months of study enrollment (a response of "yes" to question 4 or 5 on the suicidal ideation portion of the Columbia Suicide Severity Rating Scale \[C-SSRS\]), or who is at significant risk to commit suicide at screening and at visit 2. * Subject has had previous exposure with fezolinetant. * Subject has received an IP within 28 days or 5 half-lives, whichever is longer, prior to screening. * Subject is unable or unwilling to complete the study procedures. * Subject has any condition which makes the subject unsuitable for study participation. * Subject or relative is the investigator or other site staff directly involved in the conduct of the study. * Subject is an employee of the sponsor, contract research organizations (CROs) or site management organizations (SMOs). * Present or previous history of participation in a study of the IP.