Harris County Precinct 4 Constable Mark Herman said the suspect stole from two Academy Sports & Outdoors stores within an hour.
Herman said one of the stores is near the Willowbrook Mall, and the other is at Kuykendahl and the Grand Parkway.
The deputy constable, identified as Deteryon Fontonet, spotted the suspect's vehicle and attempted to pull it over. The suspect led Deputy Fontonet on a chase that stopped in the 5300 block of Slashwood, according to Herman.
Pct. 4 deputy ambushed and shot by robbery suspect, officials say
The suspect allegedly shot at the deputy constable before running into a relative's house, according to the constable's office. Herman said he counted 16 bullet holes in the deputy's patrol unit.
Law enforcement surrounded the house and was able to take the suspect into custody on the lawn outside. A gun was recovered near the front door, which could be seen by SkyEye as it hovered overhead.
Herman said the deputy constable was taken to the hospital for injuries from shattered glass.
"Please pray for our Deputy Constable," Herman said on social media.
Herman said the suspect's family thanked deputy constables for not killing him after he was in custody.
"From what I'm hearing, (Fontonet) is going to be OK. He just needs surgery on his face. Good Lord was looking out for deputy," Herman said.
By 8:40 p.m., Herman said Fontonet was out of the hospital.
"Deputy Fontonet will have follow-up doctor visits and will be resting at home," Herman said.
Herman said the suspect is 23 years old but did not release a name.