Les Bleus are next in Guinness Six Nations action on Sunday, February 28 when they take on Scotland at the Stade de France.
Galthie and another member of France’s backroom staff have tested positive for Covid-19, with both starting isolation on Monday.
All of France’s players and the rest of the backroom staff have returned fresh negative test results.
“The coach of the France rugby team, Fabien Galthie, was diagnosed positive for Covid-19 today,” read a France statement.
“This diagnosis was established following a test this morning, in verification of a PCR test carried out the day before.
“During this test the France group tested negative with the exception of two members of the management, including Fabien Galthie.
“In accordance with the health protocol in force, the two members of the management whose isolation began yesterday (Monday) evening, will continue to isolate themselves for seven days.
“Their activities will continue to be carried out remotely. To date, no symptoms have been observed.
“An additional test on Wednesday morning at the National Rugby Centre will be carried out with the entire France group.
“Tests will be carried out at home on Friday, as well as on Sunday evening at the National Rugby Centre.”
France are due to name their 31-man squad to prepare for the Scotland game on Wednesday evening.
Galthie’s resurgent Les Bleus have won both of their Six Nations matches so far, thumping Italy 50-10 and edging out Ireland 15-13 in Dublin.