The law now goes to the Senate, which is also expected to approve it.
Exceptions to the ban could be allowed for certain festivities, like carnivals, if municipal authorities decide to grant them.
People who ignore the new law could face a fine of $20 to $35 and, or, a jail sentence of up to seven days, unless they have police permission to wear the garments.
All governing parties and the opposition agreed on the move, most on the basis that people cannot be recognised wearing the clothing.
"It's not about introducing any form of discrimination," Daniel Bacquelaine, head of the liberal MR party in the parliament, told MPs, but for cases when such clothing was "aimed at stopping people from being identified".
Ahead of the vote, Isabelle Praile, the vice-president of the Muslim Executive of Belgium, warned that it could set a dangerous precedent.
"Today it's the full-face veil, tomorrow the veil, the day after it will be Sikh turbans and then perhaps it will be mini skirts," she said.
"The wearing of a full-face veil is part of the individual freedoms [protected by Belgian, European and international rights laws]."
Guy Harpigny, a bishop in the southern town of Tournai, said: "Does the state really have the right to regulate the symbols of personal beliefs?"
The ban comes amid controversy in Belgium over the wearing of religious symbols in public places.
In June last year, a Belgian politician of Turkish origin joined the Brussels regional parliament wearing an Islamic headscarf in a first for the country.
Opponents of such religious symbolism distributed flyers at the entry to the assembly building as Mahinur Ozdemir, 26, was sworn in.
Nicolas Sarkozy, the French president, has spoken out in favour of a full ban on the face-covering veil as the government draws up a law to prohibit the garment in public spaces.
According to a government spokesman, Sarkozy told a cabinet meeting earlier this month that the veil "hurts the dignity of women and is not acceptable in French society".
Belgium's upper house now has two weeks to raise any objections to the decision.