Sheriff's spokeswoman Christina Garza says Jimenez fell to the ground and struck his head after the Taser was used on him.
Authorities say the deputy had pulled over a pickup for an alleged traffic violation at about 6pm Monday when the man hit the deputy in the chest and tried to run away.
The deputy, on the Harris County Sheriff's Department force since 1991, was also taken to an area hospital where he was treated and released.
The case is being investigated by the HCSO's Homicide Unit. The cause of death for Jimenez will be determined by the Harris County Institute of Forensic Sciences.