The former British No 1 and three-time Grand Slam champion is now the British No 23.
Murray, 31, had hip surgery in January after being out of action since last year’s Wimbledon, when he lost to Sam Querrey in the quarter-finals.
He has played just three matches since then. He lost to Nick Kyrgios at Queen’s, before taking a wildcard to enter the Eastbourne International, where he beat Stan Wawrinka in the first round and then lost to Kyle Edmund.
Murray is now due to start his American hardcourt season at the Citi Open in Washington on 30 July.
Edmund retains his position as British No 1 with a career-high ranking of 16.
The other British players sat above Murray are Cameron Norrie (77), Liam Broady (177), Jay Clarke (225), Dan Evans (323), James Ward (333), Alexander Ward (338), Edward Corrie (446), Tom Farquharson (479), Brydan Klein (498), Lloyd Glasspool (538), Jonathan Gray (589), Billy Harris (679), Ryan James Storrie (698), Luke Bambridge (706), Oliver Golding (728), Evan Hoyt (745), Neil Pauffley (746), Ryan Peniston (769), Finn Bass (787), Richard Gabb (811) and Luke Johnson (825).