
The Scot, ranked 14th, has not played since May 15. If he returns at the Montreal Masters starting August 4, he will be pushing his absence to the three-month mark.
Murray, who rose to the Top ten for the first time before sliding back due to lack of play, missed the French Open and Wimbledon.
He has been testing the injury this week at the Bollettieri academy in Florida.
His website made the scheduling announcement: "Andy won't play any part in the Legg Mason Tennis Classic this coming week. He's pulled out of the tournament in order to focus on continuing the rehab to his wrist.
"He's looking ahead positively to the Masters Series event in Montreal."