Four members of the hospital staff came to the deputy's aid and helped apprehend the inmate during the ensuing struggle.
"It could very well have escalated," a spokesman for the Houston Police Department said outside the hospital Wednesday. "That's why I want to commend the hospital staff for assisting in getting this inmate in custody."
The officer, a 36-year veteran of the force, was taking the inmate to the bathroom on the hospital's fifth floor around 4:30 p.m. when the inmate, who was there for a clinic visit, went for his gun.
The inmate was detained and the officer was treated by deputies at the hospital. He suffered a through-and-through gunshot wound to his left hand, meaning that the bullet left entry and exit wounds, an HPD spokesman said.
There are no other known injuries reported at this time.
Ben Taub Hospital is located inside Texas Medical Center, which bills itself as the "largest medical city in the world."
This is a developing story. Check back for updates.