0659 GMT October 17, 2021
The world number two, 34, was scheduled to face Australia's Alex de Minaur at Melbourne Park on Tuesday, BBC reported.
Nadal said he hoped to play for 2020 runner-up Spain against Greece on Thursday.
Novak Djokovic earlier gave defending champion Serbia a winning start.
World number one Djokovic beat Denis Shapovalov 7-5 7-5 as Serbia claimed a 2-1 win over Canada in its opening Group A match.
Milos Raonic had put Canada ahead with a 6-3 6-4 win over Dusan Lajovic but Djokovic and Filip Krajinovic won the doubles match against Raonic and Shapovalov 7-5 7-6 (7-4).
Defending Australian Open champion Djokovic has won all 10 singles and doubles matches he has played at the ATP Cup, which was introduced to the tennis calendar in 2020.
US Open champion Dominic Thiem had a disappointing day as Austria lost 2-1 to Italy.
World number three Thiem, who reached the final of the Australian Open last year, was beaten 6-2 6-4 by 10th-ranked Matteo Berrettini.
Compatriot Denis Novak beat Fabio Fognini 6-3 6-4 but the Italians paired up for the doubles match to beat Novak and Thiem 6-1 6-4.
The men's team event, which has been reduced to 12 teams from 24, is being played at the same time as five other tournaments at Melbourne Park this week after a strict quarantine for all players who arrived in the country for the Australian Open.