The 28-year-old Argentine defender played 93 league matches for them after initially joining from Italy's US Palermo on loan in 2013 and then signing a permanent deal.
"We would have very much liked to continue working together," said Werder sports director Frank Baumann in a statement on Thursday. "He fully identified with Werder and always gave it everything. Unfortunately we could not agree on a new contract."
Garcia said he would have also liked to have stayed at the northern club.
Werder are in eighth place in the league and are battling for a Europa League spot with two games left.
(Reporting by Karolos Grohmann)
