Yankov, who has scored five goals in 33 internationals, picked up the injury during his club Rostov's 4-0 win over Spartak Moscow in the Russian championship on Monday.
Bulgaria coach Lothar Matthaeus was already without suspended winger Martin Petrov, while defender Petar Zanev and midfielder Hristo Yanev are doubtful after coming off in Litex Lovech's league match last weekend with injuries.
The March 26 match pits Matthaeus against his former Bayern Munich manager Ottmar Hitzfeld, now the Switzerland boss.
Montenegro top the standings with 10 points from four matches, three ahead of England, who have played one game fewer. Switzerland and Bulgaria have three points from three games, while Wales are bottom of the group with no points.
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