The Czechs, who have qualified for their seventh straight European Championship, face Croatia, England and Scotland in Group D.
"A sports tragedy for Lukas Provod," tweeted Slavia boss Jaroslav Tvrdik, adding that the 24-year-old would undergo a surgery in the coming days.
Provod, a permanent fixture in the midfield at Slavia which reached the Europa League quarter-finals this year, limped off the pitch after 19 minutes of Sunday's league game at Sigma Olomouc.
Provod has played seven games for the Czech Republic and scored one goal, in a surprise 1-1 draw against top-ranked Belgium in a World Cup qualifier in March.
Standout matches today