Police said the man made movements suggesting he had a weapon, though he turned out to be unarmed. The officers' shots missed him, and he was eventually brought down by a stun gun.
Authorities identified the man as Glenn Broadnax, 35, of Brooklyn. He faces multiple counts including menacing, riot, criminal possession of a controlled substance, and resisting arrest. He was in custody, and The Associated Press couldn't locate a phone listing for his home.
The encounter happened just before 10 p.m. near the Port Authority Bus Terminal, a block away from Times Square.
Officers saw a man on foot weaving through traffic and sometimes blocking vehicles.
"It appeared he wanted to be struck by cars," Police Commissioner Raymond Kelly said at an early morning news conference.
As officers approached, police said, the man reached into his pocket as if grabbing a weapon, and two officers fired a total of three shots. The bullets struck a 54-year-old woman in the right knee and a grazed a 35-year-old woman in the buttocks, police said.
Photos and video taken by onlookers showed a chaotic scene. Several officers tried to contain the man as he moved through an intersection, and he was finally brought down as people in the crowd yelled at police not to shoot him.
Broadnax was taken into custody after a sergeant subdued him with a Taser, police said. He was taken to Bellevue Hospital, where he was in stable condition, police said. Authorities described him as "emotionally disturbed."
The women were taken to hospitals, where they both were listed in stable condition, according to police. Neither had injuries considered life threatening, police said.
The officers who fired their weapons had been on the force for 1 ½ years and 3 years, police said.
Police did not release the names of the women.
In August 2012, nine people were injured from bullets fired by police in a confrontation with a gunman near the Empire State Building. They were hit by stray bullets, ricochets and fragments, suffering non-life-threatening gunshot and graze wounds. Officials at the time defended the officers' decision to fire on a street crowded with people.
Police guidelines tell officers to avoid unnecessarily endangering innocent people. But police are allowed to use deadly force when faced with an imminent threat of serious injury or death.
On Sunday morning, several police vehicles and half a dozen officers were still stationed outside the bus terminal at the intersection of 42nd Street and Eighth Avenue, but the area was busy as usual, with crowds of tourists.