According to federal officials, Alvin Leon Roundtree, 51, has been charged in connection with Monday afternoon's shooting on Fort Sam Houston.
Roundtree is accused of shooting his common-law wife, an instructor at the school, multiple times following an argument.
According to the criminal complaint filed jointly by FBI and San Antonio police officials, and U.S. Attorney Robert Pitman, Roundtree approached the woman Monday afternoon in the Army Medical Center and School on Fort Sam Houston to discuss their recent separation.
Investigators said following an argument regarding her decision to leave him, Roundtree pulled out a .45-caliber pistol and shot her multiple times.
"It started out as a conversation. He came into her office space, and then she took him outside of the building," said Col. Randy Anderson, Commander AMMED Center and School, on Monday.
Roundtree fled the scene of the shooting, but was subsequently apprehended on Fort Sam grounds later that afternoon.
He remains in federal custody, charged with domestic violence violation.
Roundtree faces up to 20 years in federal prison and a maximum $250,000 fine.
As of Tuesday afternoon, the woman's name had not been released. She remains in stable condition following surgery at San Antonio Military Medical Center, officials said.