Murray’s older brother Jamie claimed on Sunday evening that the world number one was suffering from a "tear" in his right elbow, with a report in the Telegraph suggesting he could be sidelined until the Madrid Masters in May.
The 29-year-old has not played since a surprise defeat to Vasek Pospisil at Indian Wells earlier in March.
Dan Evans and Kyle Edmund will fill the Murray-shaped singles void in Rouen, Normandy, while Jamie Murray will partner Dominic Inglot in the doubles.
"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," said GB captain Leon Smith.
"I know that he would really want to be here with the rest of the team.
"In Dan and Kyle we have two top 50 singles players who are improving all the time on the tour and both with games capable of upsetting higher ranked opponents. Jamie and Dom once again combine as our doubles team and will draw much confidence after performing so well recently to win key rubbers against Serbia and Canada."
Smith’s side must down a France side who can call upon the likes of Jo-Wilfried Tsonga, Gael Monfils, Lucas Pouille, Richard Gasquet and Gilles Simon – all of whom are in the world’s top 25 – and doubles world number one Nicolas Mahut.
The tie runs from April 7-9.
Read the original article on Eurosport: Andy Murray out of GB’s Davis Cup clash with France