The 31-year-old Arsenal star has had an injury-plagued career but looked in fine form in the opening half before not reappearing for the second and Bilek said that it looked potentially to be a tournament ending one.
"Tomas Rosicky picked up an injury and while its hard to tell the exact nature of it at the moment it's unpleasant, we have to hope he'll be all right," said Bilek.
Rosicky, nicknamed the 'Little Mozart', came into the tournament suffering from a calf injury dating back to the last Premier League game of the season last month but was passed fit prior to the opening 4-1 defeat by Russia.
The Czechs victory lifted them onto three points with one match remaining in the group against co-hosts Poland, who are playing Russia later on Tuesday, while Greece are struggling to reach the last eight with just a point.
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