"Due to a back injury that has bothered me for the past few weeks, the doctors have advised me to rest for the next two weeks", writes Nagal on Instagram, according to TV4 News.
The 27-year-old is ranked 82nd in the world in tennis and defeated Sweden's number one Elias Ymer in the Swedish Open this summer. Ymer is ranked 236th.
Without Nagal, India can come to Stockholm and the Royal Tennis Hall with 328th-ranked Ramkumar Ramanthan and Siddarth Vishwakarma, ranked 592nd, in singles.
Sweden will compete with, in addition to Elias Ymer, Leo Borg in singles and André Göransson and Filip Bergevi in doubles.
The team also includes debutant Adam Heinonen.
The winner of this weekend's qualifying match will get to stay in the top division of the tennis tournament.
