This is an open-label (physician and participant will know the name of the assigned drug), multi-center, non-randomized, drug/drug interaction study of JNJ-38518168 in participants with rheumatoid arthritis (RA) on a stable oral methotrexate (MTX) dose (7.5-25 mg). The treatment phase will last 16 days. Participants will be housed in the clinic for dosing and study procedures from Day -1 to Day 2 and again from Day 14 to Day 16. Participants completing treatment will have a follow-up visit between Days 22 and 25. Participants who discontinue the study prematurely will complete the Day 22 to 25 follow-up procedures at the time of discontinuation or as soon as possible thereafter. The duration of participation in the study for an individual participant will be up to 7 weeks (including screening). Participant safety will be monitored. Day 1: A single oral dose of the participant's weekly methotrexate dose. Days 2-15: Weekly MTX co-administered with two 50-mg capsules of JNJ-38518168, administered daily.