The 20-year-old, considered one of the best young players in the Balkan country, faces two months on the sidelines after sustaining the injury during Botev's 6-0 win over Neftochimik Burgas in the Bulgarian Cup last week.
Nedelev will join Bundesliga side Mainz 05 on a four-and-a-half year contract at the end of the year.
Bulgaria, who have not reached the World Cup finals since 1998, visit Armenia on Oct. 11 and host Czech Republic four days later in their final qualifiers for next year's tournament in Brazil.
Playoff hopefuls Bulgaria are second in Group B with 13 points from eight matches, seven points behind Italy who have already qualified for the finals. Denmark are third on 12, followed by Czech Republic and Armenia on nine.