"I'm in favour of compulsory vaccination for certain professional groups - that's what we need," Bavarian state leader Markus Soeder told 'Bild TV'.
"I think it would be a good signal if we discuss something like that for the football sector as well - as a signal of unity between fans and players," he said.
Only fully vaccinated fans are allowed into football stadiums in Bavaria, while players only have to show a negative test result, Soeder said.
The weekly recorded incidence of the virus in Germany hit a new high on Tuesday, one day after surpassing 300 out of every 100,000 people, the first time it has crossed the threshold since the beginning of the pandemic.
The alarming figures are fuelled in part by sluggish vaccination rates.
Around 90 percent of footballers in Germany's top two leagues are fully vaccinated - a much higher figure than the 67.6 national average.
But last month, Germany midfielder Joshua Kimmich sparked debate about whether or not it should be mandatory for footballers to be vaccinated by admitting he had opted out for "personal concerns".
The Bayern Munich star was one of five players quarantined last week while on international duty with Germany after club team-mate Niklas Suele - who is fully vaccinated - tested positive for the virus.
On Tuesday, Kimmich, as well as Bayern team-mates Serge Gnabry, Jamal Musiala and Eric Maxim Choupo-Moting all left quarantine and took part in training.
Only Suele, who has light symptoms, remains in house quarantine and misses the Bavarian giant's league game at Augsburg on Friday.
Bayern's CEO Oliver Kahn has made the club's position clear by insisting "our players ought to be vaccinated".
Only a handful of Bayern stars have opted not to be vaccinated and Kahn says those concerned are "now thinking very, very hard", because the consequences of their scepticism are "not insignificant".
However, Cologne coach Steffen Baumgart warned against mandatory vaccinations in professional German football.
"It's the wrong approach. Why should there be compulsory vaccinations for footballers and not for care workers, who have daily contact with people?" Baumgart told reporters Tuesday.