The couple who are both in their 30s are suspected of having allowed the procedure to be carried out on their 3-year-old sometime between January and April 2012 in either Sweden or Gambia.
Female genital mutilation has been illegal in Sweden since 1982. Since 1999 it is an offence even if the procedure is performed in a different country and carries a penalty of up to four years imprisonment.
If the offence results in a serious threat of death, such as a serious illness the penalty can be extended to between two and ten years in prison.
During the almost 30 years that FGM has been banned in Sweden, only 46 suspected cases have been reported, according to a report from Uppsala University published last year.
The mutilation is often done on the quiet and is difficult to detect.
Only two people have been convicted for female genital mutilation, and in both cases it was the afflicted girls themselves who raised the alarm.
In 2006 sentenced a 41-year-old man was sentenced to two years in prison for the genital mutilation of his daughter. The then 12-year-old girl was subjected to the procedure sometime in the autumn 2004.
In the second case, the same year, a 42-year-old woman was sentenced to three years in prison for sexual mutilation and gross violation of integrity of her daughter.
During the trial, the girl told of how her mother and two other women held her down while they cut away parts of her genitals.
The assault came to light when she told a school counsellor five years later.