The main goal of this trial is to learn more about the safety and tolerability of Lu AG09222 when taken together with ubrogepant. This includes looking for any new or worsening medical issues the participants have with the treatment. During the trial, participants with migraine will receive ubrogepant oral tablets and an injection of either Lu AG09222 or a placebo.

Inclusion Criteria:

• The participant has a diagnosis of migraine as defined by ICHD-3 guidelines confirmed at the Screening Visit.
• The participant has a history of migraine onset ≥12 months prior to the Screening Visit.
• The participant has ≥2 migraine days and headache occurring on <15 days per month for each month within the past 3 months prior to the Screening Visit.
• The participant has a body mass index (BMI) ≥18.5 and ≤ 35 kilograms per meter squared (kg/m^2) at the Screening Visit.

Exclusion Criteria:

• The participant has previously been dosed with an anti-pituitary adenylate cyclase-activating peptide (PACAP) treatment.
• The participant has participated in a clinical trial <30 days prior to the Screening Visit.
• The participant has taken any investigational medicinal product (IMP) <3 months or <5 half-lives of that product, whichever is longer, prior to Visit 1.
• The participant is pregnant, breastfeeding, intends to become pregnant, or is of childbearing potential and not willing to use adequate contraceptive methods.
• The participant has known or suspected hypersensitivity or intolerance to the IMP, auxiliary medicinal product (AxMP), or their excipients.

Note: Other inclusion and exclusion criteria may apply.