Hidradenitis suppurativa (HS) is a chronic and often painful inflammatory skin disease which includes the forming of lumps, abscesses and scars in areas of the skin such as under the breasts, under armpits, inner thighs, groin and buttocks. Despite the clinical benefit anti-tumor necrosis factor (TNF) therapy offers to patients with HS, there remains a significant unmet medical need for patients who fail to achieve adequate benefit with anti-TNF therapy. This study will compare lutikizumab (ABT-981) versus placebo for the treatment of adult participants with moderate to severe HS who have failed anti-TNF therapy. Lutikizumab (ABT-981) is an investigational drug being developed for the treatment of HS. In the Main Study, participants will be put in 1 of 4 groups, called treatment arms. There is a 1 in 4 chance that participants will be assigned to placebo. Around 160 adult participants with moderate to severe HS who have failed anti-TNF therapy will be enrolled in the study at approximately 50 sites worldwide. In the Sub-study, participants will be put in 1 of 2 groups, called treatment arms. Both arms will receive treatment at different dosing intervals. Around 40 adult participants with moderate to severe HS who are naïve to biologic therapy will be enrolled in the study at approximately 20 sites. In the Main Study, participants will receive subcutaneous injections of lutikizumab (ABT-981) or placebo every week for 16 weeks. In the Sub-study, participants will receive subcutaneous injections of lutikizumab (ABT-981) every week for the first 15 weeks, then either every week or every other week for 36 weeks. There will be an optional Long Term Extension (LTE) for participants who completed Week 52 of the Sub-study and, as confirmed by the investigator, have shown a therapeutic benefit to study drug. Participants would then received lutikizumab using the same assigned dosing regimen as that from Period 2 of the Sub-study for an additional 104 weeks. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic. The effect of the treatment will be checked by medical assessments, blood tests, checking for side effects and completing questionnaires and diaries.