Senior Muslim politician, Muhammad Afzal, is accused of making the comments at a meeting with Chair of Muslim Women's Network UK, Shaista Gohir.
She then wrote a letter of complaint to Birmingham Central Mosque, where Mr Afzal is chairman, claiming he said that "domestic violence was happening mainly in the Christian community because they get drunk".
Mr Afzal has served as a Labour councillor for 30 years.
He is also accused of saying domestic violence was mainly committed against men.
Ms Gohir's complaint letter also said: "We argued that although men did suffer from domestic violence, by far the larger number was made up of women.
"I explained that the problem was also significant in Muslim communities and that women have been murdered as a result. However, Mr Afzal questioned why he had not heard about these murders in the media if they had taken place.
"We explained that cases had been reported in the media and that, in fact, there had been several murders in the West Midlands alone.
"By the end of the conversation it was clear that the trustees, and especially Mr Afzal, were not interested in women's issues and had little, if any, intention of working with us on any women's rights and issues."
Mr Afzal has not commented on the claims.