The objectives of the study are to evaluate the safety, tolerability, and efficacy of 3 doses of AVP-923 (dextromethorphan \[DM\]/quinidine \[Q\]) capsules containing either 45 mg DM and 10 mg Q (AVP-923-45) or 30 mg DM and 10 mg Q (AVP-923-30) or 20 mg DM and 10 mg Q (AVP-923-20) compared to placebo, for the treatment of central neuropathic pain in a population of participants with multiple sclerosis (MS) over a 12-week period. The MS participant population enrolled includes participants with relapsing-remitting multiple sclerosis (RRMS) and participants with secondary progressive multiple sclerosis (SPMS).