A Study in Participants With Moderate to Severe Psoriasis

Inclusion Criteria Common to Both Part A: * Participant must have active plaque psoriasis covering at least 10% body surface area and a PASI score of at least 12 at screening and at randomization. * Participant is a candidate for systemic therapy * Participant has a Static Physician's Global Assessment (sPGA) score of at least 3 at screening and at randomization Inclusion Criterion Specific to Part B * Participant has completed the treatment period for part A (at least through week 20) Inclusion Criterion Specific to Part C * Participant has completed the treatment period for part B Exclusion Criteria Common to Part A, B and C: * Participant has pustular, erythrodermic and/or guttate forms of psoriasis * Participant has had a clinically significant flare of psoriasis during the 12 weeks prior to study entry * Participant has recently used any biologic agent/monoclonal antibody within the following washout periods: etanercept \>28 days, infliximab or adalimumab \>56 days, alefacept \>60 days, ustekinumab \>8 months, or any other biologic agent/monoclonal antibody \>5 half-lives prior to baseline * Participant has received systemic psoriasis therapy (such as psoralen and ultraviolet A \[PUVA\] light therapy, cyclosporine, corticosteroids, methotrexate, oral retinoids, mycophenolate mofetil, thioguanine, hydroxyurea, sirolimus, azathioprine) or phototherapy (including ultraviolet B or self-treatment with tanning beds) within the previous 4 weeks; or had topical psoriasis treatment within the previous 2 weeks prior to randomization (exception: class 6 \[mild, such as desonide\] or 7 \[least potent, such as hydrocortisone\] topical steroids will be permitted for use limited to the face, axilla, and/or genitalia) * Participant has donated more than 500 mL of blood within the last month * Participant has another serious disorder or illness * Participant has suffered a serious bacterial infection (for example, pneumonia, and cellulitis) within the last 3 months * Participant has a history of uncontrolled high blood pressure * Participant has clinical laboratory test results at entry that are outside the normal reference range * Participant is currently participating in or were discontinued within the last 30 days from another clinical trial involving an investigational drug * Participant is a woman who is lactating or breast feeding * If a participant is a woman and could become pregnant during this study, she must talk to the study doctor about the birth control that you will use to avoid getting pregnant during the study * If a participant is post menopausal woman, she must be at least 45 years of age and have not menstruated for the last 12 months * If a participant is a woman between 40-45 years of age, test negative for pregnancy, and have not menstruated during the last 12 months only, she must have an additional blood test to see if you can participate * If the participant is male, he must agree to reduce the risk of female partner becoming pregnant during the study Exclusion Criteria Specific to B: * If a participant experienced a serious adverse event during Part A considered possibly related to ixekizumab * If a participant experienced an adverse event during Part A that the study doctor believes continued ixekizumab treatment could cause harm to the participant. Exclusion Criteria Specific to C: * If a participant experienced a Serious Adverse Event during Part B considered possibly related to ixekizumab * If a participant experienced an adverse event during Part B that the study doctor believes continued ixekizumab treatment could cause harm to the participant.