Peruvian Pizarro, who played in Bremen from 1999-2001 and again since 2008 after stints at Bayern Munich and Chelsea, scored 18 times this season to take his Bundesliga tally to a record 160 goals.
"It was a very difficult decision for me because I have a lot of love for the team and this club," said the 33-year-old, who will make his last appearance for Bremen in a friendly on Wednesday.
"But as I move towards the end of my career I want to try something else. I still cannot say what it will be. I have a few offers that I am considering."