Having made his Bremen debut in 1999, Pizzaro had spells at Bayern Munich, Chelsea and Cologne before returning to Werder in 2018.
His biggest success came at Bayern where he won the Bundesliga six times and was in the squad which lifted the 2013 treble of league, cup and Champions League trophies.
Having made 18 league appearances - all off the bench - this season for Bremen, he retired after Monday's 2-2 draw in the relegation/promotion play-off at Heidenheim meant Werder stay in the Bundesliga next season.
Following the final whistle, Pizarro was hoisted into the air and Kohfeldt went to apologise.
"I was with him after the game and apologised that I couldn't bring him on in his last game," said the 37-year-old Kohfeldt. "The situation simply wasn't right".
The Peruvian wrote "Thanks, lads. Thanks, Werder Bremen - second division, never!" on Twitter.