Smith was hospitalized overnight at Baptist Medical Center in Jacksonville, and will not practice on Monday. His return was not announced.
"He'll be fine," said trainer Mike Ryan.
"I got on my knees and said a quick prayer for him," said running back Fred Taylor.
"It was a scary moment to see someone fall like that and not know what's going on," added wide receiver J.J. Stokes.
"He went to the hospital to have tests done," said Coach Jack Del Rio. "He had an episode of heat. It's a serious issue, but he appears to be doing fine."
The incident was a reminder of the death of Minnesota tackle Korey Stringer, who died of heatstroke at Vikings' training camp in July 2001. Stringer's wife, Kelci, has announced she is suing the team, saying it is dangerous for hold practice sessions in the summer heat.