Mr Trump wore a face mask as he entered New York-Presbyterian Hospital on Friday afternoon, staying for about 45 minutes.
US media reports say Robert Trump, 72, is seriously ill, but it is not clear why he was admitted to the facility.
He used to manage the Trump property empire's real-estate investments.
"I hope he's okay," the president told reporters en route to the hospital. "He has a tough time. He's having a tough time."
After the hospital visit, Mr Trump, 74, flew to his golf club in nearby Bedminster, New Jersey, for the weekend.