Constable Mark Herman made the announcement two days after the deputy was hospitalized on Friday.
"Deputy Zepeda's strength, courage, and determination have been nothing short of inspiring. While his recovery journey continues, today's milestone is a testament to his resilience and the incredible support he has received from his family, fellow deputies, first responders, and community members," Herman said in a statement.
ORIGINAL REPORT: 2 Harris Co. Pct. 4 deputies shot, 1 hospitalized after 'ambush' in Humble apartment complex: Pct. 4
Investigators said that Pct. 4 deputies were dispatched to a call about a man firing a weapon throughout an apartment complex located in the 15900 block of Woodland Hills Drive at about 10 p.m. on Friday.
When the deputies arrived, investigators said they were ambushed by the shooter when he opened fire on them. Multiple deputies returned gunfire, at which time the suspect retreated into an apartment unit, authorities said.
Zepeda was shot and taken to the hospital, and underwent surgery the next day.
The suspect was later apprehended after a K-9 unit bit him, authorities said, adding that the suspect is in custody at the hospital for treatment from the bite.
The suspect, whose identity authorities did not release, is charged with aggravated assault on a police officer, officials said.