The Arsenal midfielder will resume training next week and could play in the June 2 friendly versus Hungary, national team manager Vladimir Smicer told news website iDNES.cz.
"Maybe he will be ready for the match against Hungary but we want the bruise on the calf muscle to be healed completely so he is entirely fit for the tournament," Smicer was quoted as saying.
The Czechs are counting on Rosicky, once dubbed "Little Mozart" because of his ability to orchestrate the midfield, to lead them at next month's finals in Poland and Ukraine.
Rosicky, 31, has scored 20 goals in 85 appearances for hios country.
Czech Republic are in Group A alongside co-hosts Poland, Russia and Greece.