The Olympic tennis tournament takes place at Roland Garros from 26 July to 4 August.
Murray is a two-time singles gold medallist, triumphing in 2012 and 2016 to become the first male tennis player to win two Olympic golds.
He also won mixed doubles silver with Laura Robson in 2012.
He told the BBC on Wednesday that Paris is the “right time” for him to retire, having struggled with injuries over the past few years.
Murray won the 2012 US Open and two memorable Wimbledon titles in 2013 and 2016.
He finishes his singles career having won 46 ATP Tour titles, including 14 Masters 1,000 events.
Murray’s withdrawal means Jack Draper, Cameron Norrie and Dan Evans are the British representatives in the men’s singles draw.
Joe Salisbury and Neal Skupski are also in the men’s doubles draw along with Murray and Evans.
Katie Boulter is the sole British representative in the women’s singles and will team up with Heather Watson in the women’s doubles, with her partner also playing the mixed doubles alongside Salisbury.
More to follow.