Cilic, ranked No 9 in the world after his Flushing Meadows success, was due to kick off his 2015 campaign at the tournament on the east coast of Australia.
Tournament director Cameron Pearson said the Croatian star had ‘lost his race against time to regain full fitness’ but there was no indication about whether he would be able to participate in the Australian Open, which starts on January 19 in Melbourne.
He has been bothered by the problem for nearly six months, but it did not stop him beating Roger Federer and Kei Nishikori on the way to winning his first Grand Slam tournament in August.
Cilic withdrew from a number of events after New York but did still win the Kremlin Cup in Moscow in October before losing all three of his matches at the season-ending ATP World Tour Finals in London.
The field for the Brisbane International, which begins on Monday, includes Federer, Nishikori, Milos Raonic and Grigor Dimitrov.