"I would like to thank all those who treated and took care of Nick," Starmer added.
"Their skill and compassion is very much appreciated."
Conservative leader Kemi Badenoch expressed her condolences to the Labour leader.
"This is such awful news. Particularly devastating at Christmas time," she wrote on X.
Nick Starmer had learning disabilities from complications during birth and struggled to hold down a steady job.
In a biography of the prime minister published this year, Keir Starmer opened up about his relationship with his brother and the difficulties he faced during his childhood.
"I'm not sure he even sat exams, so he had nothing to show for coming out of education," Starmer told author Tom Baldwin. He said his brother was bullied and was often called "thick" or "stupid" at school.
"Nick was dealt a very different set of cards to me and he's had problems all his life - problems I've never had to face," Starmer said.
In his speech to the Labour Party conference in September, he said their father had often told him that "your brother has achieved just as much as you, Keir".