It happened near the hospital's trauma center on Wednesday at about 4:20 p.m.
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Authorities identified the inmate as 35-year-old Thaddeus Lewis, who is charged with aggravated assault against a public servant.
According to the Houston Police Department's Homicide Division Special Investigations Unit, the deputy was guarding Lewis, who was at the hospital for a doctor's appointment, and escorted him to the restroom.
While in the restroom, Lewis attacked the deputy, leading to a struggle, HPD said.
During the fight, authorities said Lewis grabbed the deputy's gun, and it went off.
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The deputy was shot in his left hand. According to authorities, four hospital staff members acted fast and helped detain Lewis.
Investigators said the injured deputy is a 36-year veteran of the department.
Lewis was transported back to the Harris County Joint Processing Center.