The officer had been nearby when Julie Abbott was shot Friday in the building's parking lot, and he found a man standing over her with a gun in his hand, San Antonio police spokesman Gabe Trevino said.
The officer ordered the man to drop the gun, then fired several rounds when the suspect advanced toward him, authorities said.
The suspect was listed in critical condition after undergoing surgery, University Hospital spokesman Leni Kirkman said. Authorities said they were withholding his name pending formal charges.
Abbott, 47, died at the same hospital, according to a statement from San Antonio police. Officer Michael Blanquiz, who shot the suspect, was not injured and was placed on administrative duty.
Authorities did not know a possible motive for the killing.
Abbott's name was listed on a placard outside the offices of iMED Internal Medicine on the building's first floor. According to the iMED Web site, Abbott attended medical school at the University of Texas Health Sciences Center at Dallas.
There was no answer at a phone listing for Abbott.