The 82-year-old Palmer had been on the Bay Hill course and made a television appearance earlier in the day but left before the end of the Arnold Palmer Invitational.
He had been monitoring his blood pressure after recently changing his medication, said Alistair Johnston, a member of Palmer's management team.
Palmer's doctor recommended he go to a nearby hospital for closer monitoring and Johnston said he had been instructed to stay overnight.
The seven-times major winner normally presents the trophy to the winning golfer on the 18th green.
"About 15 minutes prior to the end of play, he had gone out for what was a routine test...and the blood pressure was at a level where the doctor involved suggested that he go immediately to get more intensive evaluation at the hospital," Johnston said.
"I just tallked to his daughter, Amy, who is with him and I think the blood pressure situation is starting to ameliorate and is improving. Nobody is overly concerned about the prognosis although he is going to remain in the hospital overnight for observation."