The band said on social media that the decision was made "due to the events" in Poland between Tuesday and Wednesday.
"We hope to return to Poland next year," the post added.
The Warsaw show, scheduled for Thursday, had been part of Mogwai's 13-nation tour, which also includes Croatia, Switzerland, Germany, Greece, Turkey, Brazil, Chile and Argentina.
Formed in Glasgow in 1995, Mogwai topped the UK Albums Chart in 2021 with its 10th album As the Love Continues.
The band’s lineup includes guitarist and vocalist Stuart Braithwaite, multi-instrumentalist Barry Burns, bassist Dominic Aitchison and drummer Martin Bulloch.
(mk/gs)