Mueller-Wohlfahrt, a respected doctor, had been in charge since 1977 and has also treated many other top global athletes, including sprinter Usain Bolt while also being the German national football team doctor.
"After the Champions League game at Porto for unexplained reasons it was the medical department that was chiefly blamed for the defeat," Mueller-Wohlfahrt said in a late night statement on Thursday.
He said "the relationship of trust has been permanently damaged."
Bayern made a brief statement on his departure prior to their weekly news conference with coach Pep Guardiola, saying they "regretfully took note" of his decision.
"Especially Dr. Mueller-Wohlfahrt, but also his team, have in the past years offered the club and its players first rate work. For that we are expressly thankful," the club said in a statement.
Bayern have been struggling with injuries in recent weeks with Bastian Schweinsteiger, Franck Ribery, Arjen Robben, Medhi Benatia and David Alaba all missing in their loss to the Portuguese team on Wednesday.
The ties with Guardiola who took over in 2014 were tense from the first season with midfielder Thiago Alcantara being sent for treatment to Barcelona by the Spanish coach without consulting the team doctor.
The most recent incident was involving Ribery. The player was initially ruled out for a few days with an injury but the winger has already missed the last five weeks.
"It was his decision to leave," Guardiola told reporters. "I respect his decision. That is all."
Mueller-Wohlfahrt's resignation comes at a crucial time for Bayern, who are chasing a treble of titles, entering the crucial phase of the season.
Bayern, who are 10 points clear at the top of the Bundesliga, face Borussia Dortmund in the German Cup last four and have to overturn the 3-1 deficit against Porto in the return leg in Munich next week.
(Reporting by Karolos Grohmann; editing by Sudipto Ganguly)
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