A 21-year-old Brockton woman was stabbed in the chest Tuesday morning by a man inside the Ashmont Red Line station lobby, an attack that took place moments after the woman arrived at the station on a Brockton Area Transit Authority bus, MBTA Transit Police said.

The sudden act of violence shortly after 9 a.m. inside one of the T’s busiest subway stations — some 15,000 people use it on a daily basis — was being investigated by Transit Police who were examining surveillance camera videos Tuesday in hope of gleaning details of the attack.

“It’s highly unusual for us to have an act like this at this station,’’ said Transit Police ­Superintendent in Chief ­Joseph O’Connor.

The woman was about 4 or 5 feet inside the south ­entrance of the station when the man stabbed her in the ­upper right shoulder and chest area, officials said.

O’Connor said the man, who had been on the same bus that the victim rode to the station, approached her from ­behind.

“We can’t explain exactly what the suspect was thinking, but we do not believe that robbery was a motive,” O’Connor said.

He said the man had exhibited strange behavior before the attack.

“He was acting erratically on the bus and was interacting with some people, but nothing occurred on the bus that led the victim to believe that she was going to be assaulted,” ­O’Connor said.

Blood stains were visible inside the lobby of thestation near the ticket kiosk, which was manned at the time of the stabbing, and another 30 to 40 feet away in the pavement outside the station.

The woman was rushed by Boston Emergency Medical Services paramedics to Boston Medical Center for treatment. She was conscious after the ­attack, but her medical status was not known.

“The victim reported that she believed [the weapon] was a knife,” O’Connor said. “That’s not 100 percent confirmed.”

O’Connor described the suspect as a bearded black male in his 20s, wearing a red or maroon shirt, similar to a tank top, at the time of the ­attack. He was also wearing dark pants and dark sneakers and carrying a white plastic bag.

“We believe that our video evidence is going to lead us to identification, and that hopefully within the next few days we’ll have this case closed,” O’Connor said.