The incident happened Saturday night at a crowded intersection in Times Square, The New York Times reported.
The 35-year-old man, whose name was not reported, was darting in front of cars at the intersection. Two police officers tried unsuccessfully to corral him before opening fire.
A bullet hit one woman, 54, in the leg, fracturing her tibia and fibula, Police Commissioner Raymond W. Kelly said early Sunday. She is expected to undergo surgery later Sunday.
The other woman, 35, was grazed by a bullet on her buttocks and has since been released from the hospital, Kelly said.
The women's names have not been released.
The agitated man was in police custody at Bellevue Hospital. The extent of his injuries was not reported.
Kelly said it seemed as though the man "wanted to be struck by cars."