Those who ignore any 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.
With the governing parties and opposition in agreement, officials expect the full house to easily endorse the draft law on April 22.
"This is a very strong signal that is being sent to Islamists," said Denis Ducarme, a French-speaking deputy from the centre-right Reformist Movement that proposed the bill.
Ducarme said he was "proud that Belgium would be the first country in Europe which dares to legislate on this sensitive matter".
"We have to free women of this burden," said his colleague Corinne de Parmentier.
The vice-president of the Muslim Executive of Belgium, Isabelle Praile, warned that the move 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, she said.
Guy Harpigny, a Catholic bishop in the southern town of Tournai, said: "Does the state really have the right to regulate the symbols of personal beliefs?"
If endorsed, the vote would see the ban imposed in streets, public gardens and sports grounds or buildings "meant for public use or to provide services" to the public.
Exceptions would be allowed for certain festivities like carnivals if municipal authorities decide to grant them.
The decision comes amid controversy in the Belgium over the wearing of Muslim religious symbols in public places.
A Muslim mathematics teacher at a municipal school has been given until the middle of next week to return to her classroom after a protracted court battle to stop her wearing a simple veil there or face losing her job.
In June last year, a Belgian politician of Turkish origin was sworn in at 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.
On Tuesday, France's top administrative body ruled that there were no legal grounds for a complete ban on the wearing of full-face veils in public, but it said the burqa could be outlawed in some places for security reasons.
Staunchly secular France passed a law in 2004 banning the wearing of headscarves or any other "conspicuous" religious symbols in state schools.