It is set to be illegal for people to wear face-covering clothes in schools, hospitals and on public transport.
France and Belgium have already passed similar laws restricting what Muslim women are allowed to wear.
New Ukip leader Paul Nuttall said after his election this week that banning the burka in the UK would be one of his key policies.
Muslim women will still be able to wear burkas on public streets if they wish, but may be fined €400 if they flout the ban in specified places.
The law still has to be approved by the Dutch senate.