Wiese, who is second choice Germany keeper and is expected to be in the Euro 2012 squad, will be replaced by a new signing, Bremen General Manager Klaus Allofs said.
"Tim took this decision, Bremen had not yet decided," Allofs said. The 30-year-old's contract runs out at season end.
"We had a great time for seven years and he did his job very well but it is part of football that at some point we go our separate ways.
"We will of course sign another goalkeeper and we have already thought about it. It will be a keeper who is regarded as good and who can boost the competition (for this spot)."