The problem forced the world number one to withdraw from the Miami Open and could sideline him until the Mutua Madrid Open in May.
Murray was instrumental in his team’s triumph in 2015 but did not feature in their round one victory this year over Canada in Ottawa.
Murray crashed out in the second round of the BNP Paribas Open in Indian Wells to rank 129 Vasek Pospisil and an extended lay-off could do the world number one a world of good with the clay court season looming on the horizon.
Leon Smith, captain of the Great British team, said: “Not having Andy in the side is obviously a big loss to our team but most importantly we all wish him well for a speedy recovery back to full health and fitness.
“I know that he would really want to be here with the rest of the team.
“Facing France in a Davis Cup tie is a tough test for any group of players and this Rouen quarter-final will be no exception.”
Curious 2017 so far
Indeed, Murray’s season thus far has not been plain sailing.
After the door was left ajar at the Australian Open following Novak Djokovic’s shock round two exit, Murray was at a loss to explain his similarly stunning loss to the German Mischa Zverev.
The Scot recovered to win the ATP 500 event in Dubai last month but was forced to save seven match points against an inspired Phillip Kohlschreiber and was no doubt aided by Roger Federer’s head-scratching loss to the Russian Evgeny Donskoy.
Meanwhile, his woes at Indian Wells continue following his straight sets defeat to the Canadian and an appearance at the first Masters 1000 tournament on clay courts, Monte Carlo, has been effectively ruled out.