The unidentified man hit the deputy in the chest and then ran about 75 feet before the officer used the stun gun in Harris County Monday, the Houston Chronicle reported.
"(The suspect) fell to the ground and hit his head," Christina Garza, a sheriff's spokeswoman, said.
Paramedics performed CPR on the man as he was being taken to the hospital, where he died.
The deputy also was brought to the hospital to be examined, as he has had past medical issues.
"Our deputy was expected to be OK," Garza said.
The incident was under investigation, the newspaper reported.