The president entered New York-Presbyterian/Weill Cornell Medical Centre in Manhattan wearing a face mask.
“I hope he’s OK,” Mr Trump said shortly before arriving at the hospital. “He’s having a tough time.”
The hospital visit came ahead of Mr Trump’s scheduled weekend trip to his private golf club in Bedminster, New Jersey.
The White House did not immediately release details about why Robert Trump, 72, had been taken to hospital, but officials said he was seriously ill.
“I have a wonderful brother. We’ve had a great relationship for a long time, from day one,” Mr Trump told reporters before departing for New York.
“He’s in the hospital right now, and hopefully he’ll be all right. But he’s having a hard time.”
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.
Mary is a daughter of the brothers’ eldest sibling, Fred Trump Jr, who struggled with alcoholism and died in 1981 at the age of 43.
No family members joined Fred Jr, known as Freddy, at the hospital on the night he died, she said, adding that Donald Trump went to the movies with another sibling instead.
Robert Trump has previously worked for his older brother at the Trump Organisation.
Once a regular face in Manhattan’s social pages, he has kept a lower profile in recent years.
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%.”
