"It's a really tough decision and I love playing in Paris, but after seeking medical advice, I am not fit to compete," Murray said in a statement.
"Apologies to the organizers and thanks to everyone for the messages of support. Now my complete focus is on getting back on the court as soon as possible."
Murray retired with the injury last week in a match against Spaniard Marcel Granollers in the second round of the Italian Masters.
He fell to the Serbian superstar in the final of the Australian Open in January.