Marquez, 87, is recovering at his home in Mexico City after being hospitalized for nine days for lung and urinary tract infections.
“He is and will continue to recover at home,” the family of the author said. His wife, Mercedes Barcha, thanked the public for its support.
Marquez was born in Aracataca, Colombia, which inspired the fictional town of Macondo, the setting of his 1967 novel One Hundred Years of Solitude, for which he won the Nobel.
He was honored for “novels and short stories, in which the fantastic and realistic are combined in a richly composed universe of imagination,” the Nobel Prize committee said.
"I wish him a speedy recovery," Mexican President Enrique Peña said in a Twitter comment when Marquez was hospitalized.
"All of Colombia wishes a speedy recovery to the greatest of all time: Gabriel García Márquez," tweeted Colombian President Juan Manuel Santos.