Dose-Ranging Study of the Efficacy and Safety of TAK-101 for Prevention of Gluten-Specific T Cell Activation in Participants With Celiac Disease on a Gluten-Free Diet

The drug being tested in this study is called TAK-101. TAK-101 is being tested to treat people who have celiac disease. The study has 2 cohorts planned. Cohort 1 has 1 dose level and the Cohort 2 may include 1 or 2 additional dose levels, depending on safety, tolerability, and activity observed in Cohort 1. Dosing in the Cohort 2 will be based on data from Cohort 1. The study will enroll approximately 90 patients. In Cohort 1, approximately 45 participants will be randomly assigned in 1:2:2 ratio in one of the three arm groups which will remain undisclosed to the participant and study doctor during the study (unless there is an urgent medical need). Eligible participants in Cohort 1 will receive: * Group A: 2 infusion doses of placebo, 1 infusion dose on Day 1 and 1 infusion dose on Day 8, followed by 1 infusion dose of 25 micrograms per kilogram (µg/kg) Gluten Epitopes (GE) TAK-101 at Week 24. * Group B: 1 infusion dose of 25 µg/kg GE TAK-101 on Day 1 followed by 1 infusion dose of placebo on Day 8, followed by 1 infusion dose of 25 µg/kg GE TAK-101 at Week 24. * Group C: 2 infusion doses of 25 µg/kg GE TAK-101, 1 infusion dose on Day 1 and 1 infusion dose on Day 8, followed by 1 infusion dose of 25 µg/kg GE TAK-101 at Week 24. If it is deemed appropriate to enroll both the TAK-101 50 µg/kg GE and the 12.5 µg/kg GE dose levels in Cohort 2, approximately 45 participants may be randomly assigned in 1:2:2 ratio in Cohort 2 to receive: * Group A: Two infusion doses of placebo, 1 infusion dose on Day 1 and 1 infusion dose on Day 8, followed by 1 infusion dose of 25 µg/kg GE TAK-101 at Week 24. * Group D: Two infusion doses of 50 µg/kg GE TAK-101, 1 infusion dose on Day 1 and 1 infusion dose on Day 8, followed by 1 infusion dose of 50 µg/kg GE TAK-101 at Week 24. * Group F: Two infusion doses of 12.5 µg/kg GE TAK-101, 1 infusion dose on Day 1 and 1 infusion dose on Day 8, followed by 1 infusion dose of 12.5 µg/kg GE TAK-101 at Week 24. If it is decided not to open the second cohort at the 50 µg/kg GE dose level and if 1 2.5 µg/kg GE dose is recommended to be tested by the independent data monitoring committee (IDMC), approximately 27 participants will be randomly assigned in 1:2 ratio to receive: * Group E: Two infusion doses of placebo, 1 infusion dose on Day 1 and 1 infusion dose on Day 8, followed by 1 infusion dose of 12.5 µg/kg GE TAK-101 at Week 24. * Group F: Two infusion doses of 12.5 µg/kg GE TAK-101, 1 infusion dose on Day 1 and 1 infusion dose on Day 8, followed by 1 infusion dose of 12.5 µg/kg TAK-101 at Week 24. This trial will be conducted globally. The overall time to participate in this study is approximately 34 weeks. Participants will make multiple visits to the clinic, and will be contacted by telephone OR plus a final visit after receiving their last dose of study drug for a follow-up assessment.