The Ukip leader claimed a need to ease security fears and improve social integration were behind the ideas to be included in his party's general election manifesto.
The MEP previously said in 2013 that Ukip would not pursue a blanket ban against face-covering veils, such as a burka.
He now wants fines to be imposed on people who wear them in public, telling the BBC's Andrew Marr Show: "We have a heightened security risk at the moment and for CCTV to be effective you need to see people's faces, because whether we like it or not in this country there's more CCTV per head than anywhere else on the planet.
"We're the most watched and for that to be effective you need to see people's faces.
"Secondly, there's the issue of integration - I don't believe you can integrate fully and enjoy the fruits of British society if you can't see people's faces."
Asked why Ukip had changed from its 2013 stance, Mr Nuttall said: "There's obviously the bigger security threat that we face now.
"But you look at Trevor Phillips' report last year into Muslims in the UK, you look at the work that Dame Casey has done on this issue - integration is actually getting worse in Britain at the moment, not better. This will help."
He added that calls to ban Sharia law in the UK were designed to stop a "parallel legal system" in the country.
Questioned if he would take the same action against Jewish courts, Mr Nuttall said: "Beth Din is slightly different.
"We've had Beth Din courts in this country which date all the way back to the days of Cromwell.
"The Orthodox Jewish population is falling, it's about a quarter of a million now.
"The issue surrounding Sharia is that the Muslim population is doubling decade on decade. It's three million now, it'll be six million soon."
Asked if he would ban mosques from opening, Mr Nuttall replied: "Of course mosques will stay open.
"This isn't an attack on specifically on Muslims, it's all about integration."
When suggested people argue Ukip is seeking to become an anti-Muslim party, Mr Nuttall replied: "It cannot be right we have courts or councils in this country where the words of a woman are only worth half that of a man.
"That has no place in a liberal, democratic, functioning western democracy."