Manchester United's Varane picked up a left thigh injury in France's 2-1 defeat to Denmark in the Stade de France on Friday.
The French Football Federation (FFF) confirmed Saturday that the Manchester United defender had been a "victim of muscle pain in his left thigh".
"Tests Saturday confirmed his unavailability for the last three matches of the season," the FFF said, confirming that Konate would join the team for training in Split before playing Croatia on Monday.
France vice-captain Varane came off after an hour against Denmark and was replaced by William Saliba.
The Blues, who were leading 1-0 at that time, then fell apart, cracking in the last minutes against the Danes.
The 29-year-old former Real Madrid captain has been plagued by injuries this season with thigh and adductor problems.
His latest injury is expected to sideline him for up to two weeks.
Meanwhile uncertainty still hangs over the state of health of Kylian Mbappe, who took a knock to his left knee and was replaced as a precaution Friday evening at halftime.
Konate, 23 will finally discover the France group, thanks to a promising season with Liverpool, who reached the Champions League final, were runners-up in the Premier League and won the FA Cup and League Cup trophies.
"He is in a team that is playing for the title in the Premier League and in the Champions League, he has an interesting profile," said coach Didier Deschamps at the time of his squad announcement when he preferred William Saliba.
"There are a lot of young players who are growing, so much the better, it allows the older ones not to fall asleep," said Deschamps.
"(Konate) has all the qualities of a modern defender, but William Saliba has them too."
In addition to the trip to Croatia, the French face Austria in Vienna on June 10, then again Croatia, in Stade de France on June 13.
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