The man, who can be seen in photos released by police, first bumped into the 29-year-old woman at the Atlantic Avenue station, which sparked a dispute between them that continued onto the train, an NYPD spokesman said.
"There was a bump on the platform that created this dispute, an ongoing back-and-forth between two ladies who were actually trying to get away from him, and this man was taunting them," NYPD Chief of Detectives Robert Boyce said.
On the train, the victim took out her phone and recorded the suspect as he threatened her, police said.
The conflict escalated and he hit her with an object bound in cloth, cutting her right hand, police said.
The suspect fled the train at the Eastern Parkway station and had not been arrested as of Wednesday morning, police said.
The woman was treated at an area hospital and released, police said.
The suspect was described as standing 5-foot-9, weighing 175 pounds and was last seen wearing a black jacket, green cap and green camouflage pants with a backpack, police said.
Anyone with information should contact Crime Stoppers at (800) 577-TIPS (8477).