The world No 1 withdrew from the Miami Open because of an elbow problem and it has now been confirmed he will not be part of Britain’s team in Rouen.
Dan Evans, Kyle Edmund, Jamie Murray and Dom Inglot will take on the French on indoor clay at the Kindarena from April 7-9.
There has yet been no official update from the Murray camp on the nature of the Scot’s injury but his brother Jamie revealed at the weekend that he had a “tear” in the joint.
Murray was also suffering from a virus prior to flying home to London last week and was told to rest by doctors.
British Davis Cup captain Leon Smith said: “This is a team with significant Davis Cup experience now and these guys have all stepped up and delivered performances at the very top of the competition.
“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. They have the strongest depth of squad by far out of any nation in the competition.”
Beating France, who boast five players ranked in the top 25 in singles as well as one of the world’s leading doubles pairs, would have been a tough task even with Murray.
Without him, they will go into the match as heavy underdogs and much will depend on world number 45 Edmund.
The 22-year-old is unusual among British players in that his favourite surface is clay and he stepped up impressively in Murray’s absence from the team against Serbia last summer, winning both singles rubbers.
Evans is ranked marginally higher at 43 but has not played a match on clay in nearly two years, while his only tour-level win on the surface came in a Davis Cup dead rubber in 2013.
Smith, however, sees no reason why Evans cannot perform on clay, citing the example of Tim Henman, who reached the French Open semi-finals in 2004 having previously struggled on the red stuff.
“He learned to play on it really, really well,” said the Scot. “Dan’s serve is good on any surface, his forehand can be a weapon, he obviously moves great so I don’t see why he can’t play well on it.”
It is the same quartet that beat Canada in the first round in February, where all four played their part before the dramatic ending when Denis Shapovalov was defaulted for smashing a ball in anger into the eye of umpire Arnaud Gabas.
Britain last played France at the same stage two years ago, when Murray was the hero on grass at Queen’s Club in arguably the key victory of their title run.