The club confirmed the France international is suffering with tibial periostitis following tests carried out on Tuesday.
The news is the latest injury blow to Madrid in a season blighted by absences, particularly in defense.
Mendy has missed their past five LaLiga matches, as well as the first leg of the Champions League semi-final defeat to Chelsea, with a calf problem.
Captain Sergio Ramos, Raphael Varane, Dani Carvajal and Lucas Vazquez have been struggling for fitness in 2021 and all missed the 2-2 draw with Sevilla on Sunday.
That result allowed Madrid to move into second place in the table with three games remaining, level on points with Barcelona but ahead due to their superior head-to-head record, with Atletico Madrid two points clear at the top.
Madrid have only won three of the 10 games Mendy has missed this season in all competitions, all but one of which have been in the league.
They have taken 2.4 points per game on average with the former Lyon man in the side, compared to just 1.4 without him.