Officials said the man did not appear to be targeting Trump or others involved in the trial
"Yes he's been hospitalized," White House spokesman Judd Deer confirmed.
Trump was expected to visit his brother later in the day, Deere said.
ABC News described Robert Trump's condition as "very ill," citing unidentified sources. The nature of the illness was not known.
The US president is due to travel to his country club in nearby Bedminster, New Jersey, for the weekend.