The campaign is being launched at the start of the summer holidays, during which young girls - mainly from African communities - are thought most at risk.
Mutilation involves the partial or total removal of external female genitalia for cultural reasons.
Up to 7,000 girls in the UK are seen as at risk of this form of circumcision.
The long summer holiday is seen as the most likely time for parents to seek the procedure for their daughter as she has time to recover from what is usually a brutal ordeal before returning to school.
She can be sent abroad for the treatment, but police say they know it is also being carried out within the UK itself.
A new law was introduced in 2003, which not only repeated 1985 legislation banning the procedure, but also criminalised those who took a child outside the country for mutilation to be performed.
No-one has been prosecuted under the new legislation.
"It's a hidden act," said Alastair Jeffrey, head of the Child Abuse Investigation Command, as he announced the reward. "And that's why it's so hard to uncover.
"This is child abuse. It is not an attack on anyone's culture, it is an attack on anyone who commits this horrendous abuse of children."
Preserving purity
The police said they were anxious not to arrive at a situation where young girls returning from holidays in Africa were routinely checked at airports, and that they desperately needed grassroots support to stamp out the practice.
Female genital mutilation is practised in a number of mainly Muslim African communities, and the tradition can travel when immigrants settle abroad.
Islamic scholars say it has no justification in the Koran, and several have recently spoken out against the practice.
Yet many families apparently believe it is an essential part of initiation into adulthood and the only way to ensure their daughter is seen as "pure" and thus desirable by potential husbands.
One London youth worker within the Somali community said this was so ingrained that she had even come across young women who had wanted to be circumcised.
"You want to be part of the community," said Leyla Hussein. "You want to be married, and you don't want to be considered dirty."
There are several types of mutilation, ranging from a minor piercing of the clitoris to the complete removal of all the external genitalia.
In some cases, what remains is then stitched up with coarse thread - leaving a tiny hole, perhaps just the size of a matchstick, for urinating and menstruation.
The procedure is in most cases carried out by older women who have no medical training. Anaesthetic is rarely used and the cuts are sometimes made with the most basic of tools such as razors or even pieces of glass.
It can have a range of short and long-term consequences including infection, incontinence and infertility, as well as causing significant psychological damage.
And it can be fatal.
Egypt, where as many as 90% of women have been circumcised, has just announced a full ban on the practice after a 12-year-old girl died last month.