The gunman started shooting in the lobby of the clinic, which is part of the University of Pittsburgh Medical Center, as people screamed and scrambled to hide.
A SWAT team immediately cordoned off the area, and neighboring buildings were placed on lockdown.
According to Mayor Luke Ravenstahl, the shooter had two semi-automatic handguns, but he was killed in an exchange of gunfire with police.
The gunman has not yet been identified, and it was unclear if the shooting victims were patients, employees or family members. One of the injured was a police officer who Ravenstahl said was grazed by a bullet.
The Associated Press contributed to this report.