The Spain international, 26, is in his fourth year at the club and his existing deal had been due to expire in the summer of 2019.
Bayern lost to Real Madrid in the Champions League quarterfinals last week and crashed out of the DFB Pokal to Borussia Dortmund in the semifinals.
Johannsson, who joined Bremen in 2015, as endured two difficult years in the Bundesliga, having missed a major part of his first season with injury.
In March, Dortmund confirmed that Germany international Gotze would not play again this season as he receives treatment for a metabolic disorder.
Herculez Gomez assesses Bobby Wood's future with Hamburg amid links to the Premier League and Borussia Dortmund.
Borussia Dortmund defender Marc Bartra is happy with his continuing recovery from wrist surgery after he was injured in an attack on the team's bus.