A German footballer who told a female referee "women have no place in men's football" during a second division match could find himself officiating a girl's game as part of his punishment.

Fortuna Dusseldorf's Kerem Demirbay had to apologise to German FA (DFB) referee Bibiana Steinhaus for his comments immediately after she sent him off for a second yellow card late in his side's 2-1 win at FSV Frankfurt last weekend.

"I have apologised to Mrs Steinhaus in person and I am very pleased she accepted my apology," he said, having scored both goals on Sunday.

The DFB are investigating the incident, but Demirbay's club has already suggested an unusual punishment.

"It would be a good thing, if he really wants to prove his true opinion of women, if he goes to a girl's football match -- as a referee," said Fortuna's interim CEO Paul Jaeger.

Demirbay, 22, took to Facebook to publicly apologise to the 36-year-old Steinhaus, who officiated the 2011 women's World Cup final when Japan beat the USA in a penalty shoot-out, and also refereed the 2012 Olympic final in London.

"I am extremely sorry for what I said to Mrs Steinhaus. I should have never said this sentence, because it is not what I think of women," wrote Demirbay.