The bill, which was tabled by the nationalist Patriotic Front (PF), was backed by 108 MPs, with just eight voting against it, at its first reading on Wednesday.
Bulgaria's second-largest opposition party, the Movement for Rights and Freedoms (MRF), tried to get the reading postponed by suggesting the measures be covered in counter-terrorism legislation instead, but the move was rejected.
The law states that clothing hiding the face may not be worn in central and local government offices, schools, cultural institutions, and places of public recreation, sports and communications.
Tuncher Kardzhaliev, an MRF MP, said the bill had no value and did not solve a single major problem, the Sofia Globe reported. The way it was drafted meant it would apply to beekeepers as well as religious clothing, he said.
Those who violate the law face a fine of 200 leva (£80) for the first offence, and for second and further offences, 1500 leva and deprivation of social benefits, the website reported.
Muslims make up about 12 percent of Bulgaria's 7.2 million population and most belong to a centuries-old community, largely ethnic Turks, among whom full-face veils are not common.
The move at a national level follows a ban in several towns in Bulgaria, starting in Pazardzhik in April. At the time, the local government of the town, which has a population of 70,000 people, said it would prevent tension among communities and boost security in the wake of the terrorist attacks that shocked France and Belgium.
"I am tired to hear that Pazardzhik is the town of the burqas. We want to say aloud that we are not that, but a town of responsible people and we will be associated with other achievements," Mayor Todor Popov told the national radio.
Part of the Roma minority practices an ultra-conservative form of Islam and its women have started wearing full-face veils in recent years, angering nationalists and bewildering other residents of Pazardzhik.
Many Bulgarians are concerned that the migrant inflows into Europemay pose a threat to their predominantly Orthodox Christian culture and help radicalise part of the country's long-established Muslim minority.
In February, 13 men - most from Pazardhik's Roma minority -went on trial charged with helping people join the Islamic State group in Syria, propagating an extremist ideology and inciting to war.
France in 2010 banned full-face veils after years of debate, while in May, the Netherlands introduced a partial ban on wearing a veil in schools, hospitals and on public transport.
The subject has long been debated in Britain. In January, David Cameron, the Prime Minister, refused to endorse a French-style blanket ban but made clear that individual organisations can choose to stop Muslim women wearing the veil.
Source: The Telegraph