Inclusion Criteria:
* 18 to 70 years of age
* Weight ≥ 40 kg and BMI ≥ 18.0 kg/m2.
* History of migraine headaches with or without aura, with migraine onset at ≤ 50 years of age and for at least 12 months prior to screening.
* At least 12 MHDs over the last 3 months prior to screening.
* Participants must fulfil the following criteria for migraine in prospectively collected baseline information during the 4 consecutive weeks of baseline migraine headache data collection prior to Day 1: (a) ≥ 4 and ≤ 14 MHDs per month. (b) On ≥ 4 days, fulfils any of the following criteria: (i) migraine without aura; (ii) migraine with an aura symptom accompanied or followed by a headache within 60 minutes; (iii) probable migraine; (iv) recurrent attacks that do not match ICHD criteria for migraine but successfully respond to migraine-specific medication.
* Participants who fulfil criteria for MOH are eligible for this study.
* History of unsuccessful treatment with ≥ 2 small molecule migraine preventive treatments from different classes (a) aCGRP-N participants are eligible to receive an aCGRP therapy but must have not yet received aCGRP therapy for acute or preventive treatment at any time. (b) aCGRP-IR participants must have tried and have failed at least one aCGRP therapy used for preventive treatment.
* Participants must be able to distinguish migraine headaches from tension-type headaches.
* Female participants who are not pregnant and do not plan to become pregnant during the study, are not lactating, or are of nonchildbearing potential. FOCBP who are sexually active with a non-sterilised male partner must use adequate contraception consisting of two highly effective methods of contraception throughout the study. FOCBP must agree to comply with protocol specified guidance for safe administration of MEDI0618. FOCBP must refrain from egg donation and in vitro fertilisation from the time of signing the ICF, throughout the study, and for 10 weeks after the last administration of investigational product (IP).
Exclusion Criteria:
* History of migraine sub-types including hemiplegic (sporadic or familial) migraine, ophthalmoplegic migraine, and basilar-type migraine
* History of headache other than migraine within 3 months prior to screening.
* History of severe or ongoing allergy/hypersensitivity reactions or history of hypersensitivity to immunisations or immunoglobulins.
* History of any significant psychiatric disorder which could be detrimental to participant safety or could compromise study data interpretation.
* Presence of any clinically significant illness, such as cardiovascular, neurologic (except for non-exclusionary headaches in participants with migraine), pulmonary, hepatic, renal, metabolic, gastrointestinal, urologic, immunologic, or endocrine disease or disorder.
* History of cancer within 5 years of screening, or between screening and randomisation, with the exception of non-metastatic basal cell carcinoma of the skin, carcinoma in situ of the cervix, or non-progressive prostate cancer.
* Known history of drug or alcohol abuse within 1 year of screening or positive test for drugs of abuse or alcohol at screening or at Day -1.
* History of QT prolongation \> 450 msec (\> 470 msec for participants aged ≥ 65 years) associated with other medications that required discontinuation of that medication.
* Congenital long or short QT syndrome.
* History of arrhythmia (multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia), which is symptomatic or requires treatment, symptomatic or uncontrolled atrial fibrillation despite treatment, or asymptomatic sustained ventricular tachycardia. Participants with atrial fibrillation controlled by medication are permitted.
* Use of migraine preventive medications within 30 days or 5 half-lives (whichever is longer) prior to screening and throughout the study
* For aCGRP-N participants only: prior use of an aCGRP therapy for acute or preventive treatment.
* Use of opioids or barbiturate containing analgesic \> 2 times/month on average in the 6 months prior to screening for the treatment of pain (opioid administration in an emergency setting may be an exception).
* Use of botulinum toxin (e.g., Botox ®, Dysport®, Jeuveau™, Myobloc®, Xeomin®) for migraine or for any other medical or cosmetic reasons requiring injections in the head, face, or neck during the 4 months prior to screening.
* Use of an intervention or device (eg, scheduled nerve block, transcranial magnetic stimulation) for treatment of migraine within 2 months of screening.
* Use of prescription or non-prescription, non-biologic drugs, including vitamins and herbal and dietary supplements, within 7 days or 5 half-lives (whichever is longer) prior to screening and throughout the study unless the medication will not interfere with the study procedures or compromise participant safety; the dose and regimen must have been stable for at least 3 months prior to screening and must remain stable throughout the study.
* Requires treatment with another biological therapeutic agent including IV immunoglobulin treatment during the course of the study. Prior use of therapeutic antibodies is allowed if that use was \> 5 half-lives of the intervention or 3 months prior to screening, whichever is longer.
* Therapeutic vaccines are permitted during the study, but ideally, live attenuated vaccines should be administered \> 30 days prior to randomisation and inactivated vaccinations (eg, inactive influenza, COVID-19) should be administered \> 14 days prior to randomisation.
* Participation in another clinical study with an IP, including an experimental vaccine, or device, within 5 half-lives of the intervention or 3 months prior to screening, whichever is longer.
* Known hypersensitivity to MEDI0618 or any of the excipients of the product.
Other protocol defined inclusion and exclusion criteria may apply.
