The woman did not need medical treatment and she did not file a police report but investigators still sought out the suspect, who they believed to be Thompson, a recidivist offender, WABC reported.
Thompson has previously been arrested at least 17 times by transit police, The New York Times reported.
Thompson was arrested in May for pulling the emergency brakes on subway cars, delaying trains and affecting thousands of passengers, investigators said. He was charged with three out of 37 incidents, it is unknown if Thompson was involved the other times.
"This man put lives at risk, endangering himself, our workers and his fellow passengers while disturbing the lives of thousands of people," Shams Tarek, a spokesman for the Metropolitan Transportation Authority, told the Times in August.
In August, he was arrested for "subway surfing," riding on the outside of a subway car, the Times reported.
In Wednesday's incident, Thompson was arrested and charged with assault, felonious reckless endangerment, menacing and criminal trespassing, WABC reported.
"Enough is enough," New York City Transit Chief Andy Byford said in a statement, WNBC reported. "This individual is a criminal and it's unacceptable that he be allowed to continue to create mayhem on the subways, mayhem he admits is deliberate, that puts riders' and MTA employees' lives at risk. He should be banned from the system – period."