The 33-year-old forward has announced that he will not be signing a new contract with the club and now intends to finish his career 'by doing something different'
The Peru international had been offered a new contract by the club but has decided against accepting it in order to continue his career elsewhere.
"That was a very difficult decision for me because I feel a great love for the team and this club," Pizarro told Bremen's official website.
"But I would like to end my career by doing something different. What that is, I cannot say yet. I have some offers that I have yet to evaluate."
Pizarro has been linked with Bremen's Bundesliga rivals Borussia Dortmund, Bayern Munich, Borussia Monchengladbach and Schalke in recent weeks, while there has also been talk of lucrative offers from Qatar and the United States.
Bremen sporting director Klaus Allofs insisted that the club bore no ill will towards the 33-year-old for rejecting the opportunity to extend his stay at the Weserstadion.
"Three times we had managed to convince him to sign for Werder but it was not possible a fourth time," he explained.
"We are very sorry for that, but glad that finally a decision has been made and would like to thank Claudio for the great time we have had together."
Pizarro joined Bremen in 1999 from Alianza Lima and spent two years with the club before moving to Bayern Munich. The veteran striker returned in 2008 on loan from Chelsea before making the move permanent the following summer.