The shooting followed a dispute that occurred around 1 a.m. Saturday at a residence in the Bronx, said Officer Chris Pisano, who had no details on the dispute. The victim suffered gunshot wounds to his left hand and right knee and was taken to a hospital in stable condition, Pisano said.
No arrests have been made; the investigation continues.
The university said in a statement that Parrom, a Bronx native, had gone home to visit his mother, who is ill. The statement said he was shot but provided no details.
Wildcats coach Sean Miller said he has been in contact with Parrom and looks "forward to his return to Tucson and being back in class this week." Miller added, "Once we have more information, we'll be able to address his potential return to team activities."
One of Parrom's former coaches said the junior swingman is doing well.
Gary Charles, who coached Parrom on a youth travel team, told the Arizona Daily Star in Tucson that Parrom did not go into detail but assured him that the situation was not dire.
"He said: 'Don't worry. I'm OK. I can walk. I'm good,"' Charles told the newspaper. "That was good enough for me."
Parrom, a 6-foot-6 reserve, averaged 5.5 points and 2.5 rebounds in the NCAA Tournament last season for a Wildcats team that advanced to the Elite Eight.