Pizarro, who has been granted a farewell match, joined Bremen for a fourth time in 2015 after his second spell at Bayern Munich.
The Peru international previously joined Bremen in 1999, and had two further spells at the Bundesliga club before returning in 2015 after three years with Bayern.
Pizarro scored 16 times during the 2015-16 campaign, but he only managed one goal in 19 Bundesliga appearances last season, and will now move on after failing to land a new contract at Die Werderaner.
"We signalled to Claudio in the middle of May that we would probably not extend his contract," Baumann told Bremen's official website.
"We've incorporated many different aspects into our decision. Because of the great competition in attack and the young talent whose development we don't want to block, we have decided not to extend Claudio's contract.
"Claudio is a legend and he will get the best possible farewell for a player at Werder Bremen: his own farewell game. This honour has only been shared by a few Werderans so far."
Pizarro, who is not expected to retire despite his release, is currently the fifth-highest goalscorer in Bundesliga history on 190 goals.