Representatives of the council and local dignitaries were at the presentation, held at Parklands leisure centre, Wigston Road, Oadby on Wednesday night.
Chairman of MBCOL, Suleman Nagdi, said: "It is a matter of great pride and is just reward for the work that the volunteers have put into their work.
"I see this not just as an award for the Muslim community but for the wider community."
The council was set up in 1994 to deal with the procedures and practices surrounding the burial of Muslims.
The group, a registered charity, helps families cope with the official processes of registering a death, dealing with a coroner and organising a burial. It has also gained a national reputation for its work with government departments on issues surrounding funeral practices and its practices have been copied around Europe.
Mr Nagdi said: "This was a groundbreaking organisation when it was launched 13 years ago and we are proud of what we have achieved in that time.
"It was very humbling to hear the words of congratulation we received from everybody there, and it is testament to the work of those at MBCOL."
Abdul Osman, Leicester City Council cabinet member for community cohesion, said: "This is a very prestigious award and I congratulate MBCOL for its achievement.
"I have been greatly impressed by the work of the volunteers at MBCOL over the years.
"Many organisations around the country and Europe look to the council for guidance and that is a credit to it and a great asset for the city."
The Queen's Award for Voluntary Service was introduced in 2002 to celebrate the Golden Jubilee and to reward excellence in voluntary activities carried out by groups in the community.
The award recognises the role played by hundreds of thousands of unsung heroes.
Each organisation nominated must be shown to regularly devote its time to helping others in the community, improve the quality of people's lives and provide an outstanding service.
A spokesman for the award organisers said: "MBCOL was rewarded for its work to address the needs and requirements of the Muslim community locally, nationally and at a European level regarding procedures and practices relating to interment of the deceased."
The award was presented to Mr Nagdi by Lady Gretton, Lord Lieutenant of Leicestershire, and came in the same week MBCOL announced plans for a £1 million bereavement centre for Muslim families.