Nadal, in Team Europe coached by Björn Borg, would have met Australian Nick Kyrgios in singles before the doubles match with Federer against John Isner and Jack Sock.
"I'm disappointed that I can't keep playing, it's been great fun," Nadal said in a statement.
The Spaniard is replaced by Stefanos Tsitsipas in the double while Dominic Thiem takes his place in the single.
This is the first time the Laver Cup is part of the official ATP program. Europe won last year in Chicago by 13–8.