The unidentified man was tackled by an officer after he was observed running from a home where a burglary had been reported, said The Houston Chronicle.
The suspect refused to stop struggling so a second officer used his Taser to subdue him, said police spokesman John Cannon.
Paramedics took the suspect to a nearby hospital where he was pronounced dead.
Homicide detectives and internal affairs officers are investigating the incident classified as an "in-custody death," Cannon said.
An autopsy will determine whether the suspect was under the influence of alcohol or drugs at the time.