The 22-year-old, who joined Serie A team Cagliari from CSKA Sofia in January, has also been ruled out of Bulgaria's visit to Kosovo on Monday.
Bulgaria coach Petar Hubchev has decided not to call up another player to replace Despodov, who was voted Bulgaria's 2018 player of the year.
England and Czech Republic are the other two teams in Group A.
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(Reporting by Angel Krasimirov; editing by Sudipto Ganguly)
