The Germany international said on Saturday he was not vaccinated because of concerns he had over long-term effects of the vaccine but added he might do it in the future.
This triggered an instant storm of criticism across Germany, with many arguing football players needed to be role models.
The German Football League (DFL) on Tuesday said more than 90% of players and staff in the top two German divisions had been vaccinated.
"It is important to say that we can only advise everyone to get vaccinated," Bayern CEO Oliver Kahn told reporters on Monday evening. "We have highlighted that through a number of actions.
"At the end of the day one has to respect that others can have a different opinion."
Critics have said Kimmich's position on vaccination also went against his actions of co-founding the #Wekickcorona organisation that financially supports charities and welfare organisations during the pandemic.
"Bayern supports vaccination actions in a sustainable way," Bayern president Herbert Hainer said. "But at the end of the day there is no vaccination obligation with us. It is an individual decision.
"Joshua Kimmich did say after all that maybe he would be vaccinated in the future. I would be happy if that happened," Hainer added.
The 26-year-old also got the backing of former Bayern CEO Karl-Heinz Rummenigge who said the player would eventually take the "right decision."
"If there is one player I know who is extremely responsible and a role model in many things in life then this has always been Joshua," Rummenigge said, who stepped down earlier this year to be succeeded by Kahn.
"In this case I think he will at some point take the right decision."
Meanwhile, Bayern's coach Julian Nagelsmann will miss their German Cup second round match at Borussia Monchengladbach on Wednesday after failing to recover from COVID-19 in time.
"I am doing alright and everything is in order," Nagelsmann told a news conference. "But unfortunately I will not be there for the Gladbach game.
"I remain in home quarantine and I have the next test on Thursday. I had a test yesterday which unfortunately did not go in a way that I could be in Gladbach," he added. "I hope it will be different on Thursday.
"I would have liked to be nearer but thanks to modern technology a lot is possible. I am happy that it has gone so well so far."
Without Nagelsmann on the bench, the Bundesliga champions beat Benfica 4-0 in the Champions League 4-0 last week, and then fired four more goals past Hoffenheim on Saturday to remain top of the league table.
In both matches Nagelsmann was replaced on the bench by his assistant Dino Topmoeller.