The Thornhill, Ont., native, who is ranked 11th in the world, said he'd hoped he would be ready when Canada begins its World Group first-round tie against Japan in Tokyo on Friday.
"This decision was very difficult to make but I believe in the players on our team and that they can get us the win," said Raonic in a statement Thursday. "With a team scenario the most important part this week is to come out with a team win and I believe this is the best way to do it."
Raonic will be replaced by fellow Thornhill native Peter Polansky.
He joins Frank Dancevic of Niagara Falls, Ont., Daniel Nestor of Toronto and Vancouver's Vasek Pospisil.
Dancevic, ranked No. 119 in the world, and the 135th-ranked Polansky will play a pair of singles matches against No. 18 Kei Nishikori and No. 140 Go Soeda.
Pospisil and Nestor will step onto the hard court at the Ariake Coliseum in a doubles match against Yuichi Sugita and Yasutaka Uchiyama.
Canada reached the Davis Cup semifinals in 2013.