The Australian world number two currently sits third in the FedEx Cup standings, 1,132 points behind leader Will Zalatoris.
Agent Bud Martin confirmed the injury was one Smith had been battling for some time.
“Unfortunately Cam will be unable to compete in the BMW Championship this week in Wilmington, DE,” read a statement.
“He has been dealing with some on-and-off hip discomfort for several months and thought it best to rest this week in his pursuit of the FedEx Cup.”
Smith is one of the many golfers linked with a potential move to the Saudi-backed LIV Golf Series.
The withdrawal follows a dramatic weekend for Smith, who on Sunday was chasing a world number one ranking and was two shots off the lead heading into the final FedEx St Jude Championship.
But an unfortunate turn of events saw him issued a two-stroke penalty for – read a PGA statement – “playing the ball from the wrong place” on the fourth hole during the third round.
He could not recover from the punishment, ultimately finishing in a seven-way tie for 13th.