In a letter sent to the corporation's director general, Mark Thompson, the MCB media spokesman, Inayat Bunglawala, said a forthcoming Panorama programme investigating Muslim organisations in Britain would "create mistrust" between Muslims and others.
The letter, sent on Thursday, said: "It appears the Panorama team is more interested in furthering a pro-Israeli agenda than assessing the work of Muslim organisations in the UK.
"It is quite regrettable that at a time when it is of utmost importance that trust is built between Muslim communities across the country and the wider society, that the Panorama team seem intent on creating mistrust by serving the interests of the pro-Israeli lobby and undermining community relations in the UK."
Mr Bunglawala accused the programme-makers of being "used by the highly placed supporters of Israel in the British media" to make political capital out of last month's terror attacks in London.
The MCB is the largest and most powerful Muslim organisation in the country. Its secretary general, Sir Iqbal Sacranie, was knighted in the Queen's Birthday honours list in June and has been a regular face on television screens since the July attacks.
More than 400 groups are affiliated to the MCB. According to The Observer, the BBC programme - to be aired next week - is thought to be critical of some of the affiliates for their links to extremists.
A BBC spokesman said last night: "The BBC rejects completely any allegations of ... bias and is confident the Panorama programme will be fair and impartial."