The 41st American president, 91, took a tumble at the family compound in Kennebunkport in the northeastern US state of Maine on Wednesday, Jim McGrath said.
“President Bush remains hospitalized at Maine Medical Center. We will send updates as they become available,” McGrath wrote on Twitter.
“His condition is stable — he is fine — but he’ll be in a neck brace.”
The hospital is in Portland, Maine, around 30 miles (50 kilometers) north of Kennebunkport.
One of his granddaughters, Jenna Bush Hager, who works as an NBC News correspondent, thanked well wishers for their support and said the family was confident he would recover.
“Thanks for all of your thoughts+prayers for our dear Gamps. We are optimistic that he will heal well,” she wrote on Twitter.
Former first daughter Chelsea Clinton also wished Bush senior a speedy recovery.
George H.W. Bush is the oldest of America’s four living presidents. He is photographed most often in a wheelchair and has seemed frail in recent public appearances.
In December he was admitted to a Texas hospital for breathing problems.
He was treated at the same Texas facility in November 2012 for bronchitis, spending nearly two months in the hospital.
He is patriarch of one of America’s most prominent political dynasties and father to former US president George W. Bush.
Another son, Jeb, the former governor of Florida, last month launched his bid for the White House in 2016 and is campaigning for the Republican nomination.
“The country saw a great leader and good man point the way to a better future. I am 1 of the 2 proudest parents in America today,” his father wrote on Twitter at the time. -AFP