The president is expected to visit his 72-year-old brother at a hospital in Manhattan on Friday, White House spokesman Judd Deere said.
Mr Trump was already scheduled to visit his property in Bedminster, New Jersey.
It is not known why Robert Trump was taken to hospital, but officials said he was seriously ill.
The president has “a very good relationship with his brother who is very special to him”, Mr Deere said.
Robert Trump recently filed a lawsuit on behalf of the Trump family seeking to stop publication of a tell-all book by the president’s niece Mary, titled Too Much And Never Enough.
The president has said her book was a violation of a non-disclosure agreement she signed in connection to a financial settlement she received from the Trump family.
Robert Trump has previously worked for his older brother at the Trump Organisation.
He married his longtime girlfriend, Ann Marie Pallan, in March, according to the New York Post. He divorced his first wife, Blaine Trump, more than a decade ago.
In a 2016 interview with the New York Post, he described himself as a big supporter of his brother’s run for the White House, adding: “I support Donald 1,000 per cent.”