Under the Laver Cup rules the referee was notified and Team Europe captain Bjorn Borg has substituted Stefanos Tsitsipas in the doubles match with Roger Federer, and Dominic Thiem will compete against Nick Kyrgios in the singles match.
Team World captain John McEnroe was notified immediately of the changes.
Nadal said: “I’ve had an amazing time playing here at the Laver Cup and I’m so disappointed I’m not able to play again today, but I have some inflammation in my hand and I need to rest.
“The atmosphere has been amazing here in Geneva and of course I’m going to be there for all my teammates and do everything I can to support them and help Team Europe win the Laver Cup.”