Rosicky, who damaged his calf in Arsenal's last Premier League Match on May 13, got the green light after the squad arrived in Wroclaw where the Czechs play their group stage matches.
"His condition is good, he is all right in terms of health," coach Michal Bilek was quoted as saying on the news website iDNES.CZ.
"I think he will play against Russia."
Rosicky, who has scored 20 goals in 85 appearances for his country, missed Czech Republic's final two warm-up matches.
His ability to penetrate opposing defences was sorely missed in the 2-1 loss to Hungary on Friday.
After playing Russia the Czechs face former European champions Greece and co-hosts Poland in Group A.