The suspension will take effect immediately, meaning the team will be without Calathes when it opens its first-round Western Conference playoff series against the Oklahoma City Thunder on Saturday night.
In a statement, the league said Calathes tested positive for Tamoxifen. Yahoo! Sports, which was first to report the suspension, said the banned substance was found in a supplement Calathes had been taking.
There was no evidence of any testosterone or performance-enhancing drugs in his test results, the website's report said.
David Cornwell, a lawyer representing Calathes, released his own statement on Saturday.
"Our tests identified tamoxifen in a supplement Nick [used] for a legitimate medical condition and our tests confirmed that Nick did not have testosterone or any other PED in his body -- thereby rebutting the presumption that he used tamoxifen to offset the side effects of testosterone use," he said. "Despite this irrefutable, objective scientific evidence, the NBA's response was, 'Oh well.'
"This is indefensible because no legitimate purpose is served by suspending a man who the NBA knows was not cheating."
Calathes averaged 4.9 points and 2.9 assists for the Grizzlies during the regular season.
Information from The Associated Press was used in this report.