FGM involves the removal of all or part of the female genitalia. Sometimes the remaining flesh is stitched closed, a practice called infibulation, leaving only a tiny opening for urination and menstruation, and making intercourse and childbirth painful.
Many human and gender rights activists say the practice puts girls under serious health risk, sometimes resulting in death.
Different levels of punishment are codified in the act for those who violate the ban. Anyone caught doing FGM on a girl will be sent to jail for 10 years - but if the girl dies during the act, a life sentence is to be imposed.
A number of African nations have outlawed the customary practice, but in many of those countries FGM is still common.
Nalule Safia Juuko, vice chair of the Ugandan Parliamentary Committee on Equal Opportunities, cautioned that the passage of this law was only a first step.
"But of course we realize as Parliament that an act alone can not do so much, given the fact that the practice has been an issue with that community for years and years," she said. "So what we also considered as Parliament yesterday, the Speaker asked the prime minister to tell us what the government is going to do in addition to passing the act," said Juuko.
She said that funds need to be allocated to run a sensitization campaign within the communities where FGM is still widespread. She also suggested that a program needs to be set up to provide an alternative income to those who act as the operation's surgeons.
She expressed strong support for the level of punishments put into the law.
"The act is providing punishments, and not simple punishments. I think people will have to re-think if they go on to practice FGM," she said.
The operation is practiced only within a few certain communities in Uganda, most of whom live in the northeastern part of the country.
The operation is usually performed on a girl at any time up until she is 15 years old.
According to the World Health Organization, up to 140 million living women globally have undergone genital mutilation. Three million girls are thought to be at risk of the procedure in Africa every year.