The Bundesliga outfit confirmed that the 22-year-old is recovering from a partial MCL tear in his left knee.
The club expect Schmid to be out of contention for "several weeks".
"It's really a shame for Romano that he suffered this injury at this stage of the season," said Clemens Fritz, head of professional football and scouting.
"He will be given all the time he needs in order to recover and return to us stronger than before."
The Austrian international has made 14 Bundesliga appearances for Werder this season, and has provided two assists from midfield.