There are currently five drop-in clinics in England for victims of the practice, which affects an estimated 200 million women and girls worldwide.
But there is no such medical provision in Wales.
Now charity Bawso is working to open a pilot clinic at the Cardiff Royal Infirmary to provide medical and psychological help to survivors.
In 2014-15 Bawso supported 788 families affected by FGM in Wales which, according to the World Health Organization involves "the partial or total removal of the female external genitalia or other injury to the female genital organs for non-medical reasons".
Bawso's violence against women director Dr Mwenya Chima said: "In the UK there are women's clinics for women who have had FGM, for medical and psychological help. Survivors can just walk in and ask for help.
"But in Wales we don't have any of that. We are trying to make a case to health agencies that we need to have this kind of clinic, even if it is initially for one day a week for a year to see if there is a demand."
Dr Chima believes there is a big gap in the support provided, and that many survivors of FGM in Wales are not known about.
She said: "I worked with a young women recently - a survivor of FGM - who wanted medical help as she was having problems. Although she wanted help she was already in two minds about having anything done as she was going against her parents.
"We tried to get her help from the clinic in Bristol, but there were delays because she was outside the area, so in the end it didn't happen and she is still living with these problems now."
The call comes as the world marks the international day of zero tolerance to FGM - a UN-sponsored event to raise awareness of the issue.
Although it has been illegal to carry out FGM in the UK since 1985, there have been no successful prosecutions relating to the practice, which is carried out for cultural and religious reasons in certain communities.

Redrow Homes South Wales has submitted plans for up to 630 houses on land north and south of Llantrisant Road, in Radyr.
An outline application for about 1,000 homes in Lisvane has been put forward by South Wales Land Developments Ltd.
Planning committee councillors will consider both applications, which are recommended for approval, at a meeting on 10 February.
A primary school and community centre are also included in the plans for both developments.
More than 90 residents have previously objected to the Lisvane proposal, which forms part of the council's Local Development Plan (LDP).

The migratory bird of prey has returned to RSPB Scotland's Loch Garten reserve, near Grantown on Spey, for its 14th season.
Nicknamed EJ, her previous drama-filled visits have included having her eggs kicked out of the nest by rival males.
Reserve staff have compared her seasons to a TV soap.

It's the fifth coin portrait to have been created during the Queen's reign.
It was unveiled in a special ceremony in London and coins carrying the new design will also begin being made from today.
But it may take a little while for the coins to get into your pockets - new coins tend to go to cash centres and banks first.

Brian Buckle of Fishguard was convicted of child sex abuse in the 1990s, when his victim was aged between eight and 10-years-old.
Swansea Crown Court sentenced him to a combined 33 years in prison, to be served over a 15 year period.
He was found guilty of 16 counts of non-recent sexual abuse against a child.
Dyfed-Powys Police Det Insp Richard Yelland said the sentence recognised "long-lasting harm" to the victim.
He added: "This is the second case for the force, in recent weeks, where a significant custodial sentence has been passed down to a perpetrator of non-recent sexual offending."
Campaigners want a dedicated clinic for victims of female genital mutilation (FGM) to be opened in Wales.
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Plans for more than 1,600 new homes in Cardiff look set to be approved.
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A female osprey whose previous breeding seasons have been described as being akin to a soap opera has laid her first egg of the 2016 season.
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A new picture of the Queen to appear on coins has been unveiled.
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A 45-year-old man from Pembrokeshire has been been jailed for historical sex offences against a child.