The measure was backed by both of the ruling parties, the SPÖ and ÖVP, on Tuesday, in spite of political turbulence that has divided the governing coalition in recent days.
Starting in October, police will be charging fines from people who wear clothes that obstruct their facial features. The 150-euro ($166) fine would also apply to women wearing burqas and niqabs at universities, courts, or in public transport.
It was not immediately clear how many people would be affected by the ban.
Austrian mainstream parties have come under pressure from a rise in popularity for the far-right FPÖ faction, which criticized the law adopted on Tuesday by saying it did not go far enough.
School of life skills and ethics
Other measures in the legislation included setting up a 12-month integration school for migrants who are deemed to have good chances of staying in Austria. The schools would offer German courses, but also teach the asylum seekers about ethics and values considered customary in the country. Other skills, like applying for a job, would also be included.
The programs would aim to provide migrants with better prospects in society, said State Secretary Muna Duzdar.
"However, it is also clear that people need to take us up on the offers we create," she was cited by the daily Wiener Zeitung as saying.
Migrants who refuse to take part in the courses would see their social welfare benefits cut.
Additionally, the law also sees asylum seekers expected to perform unpaid public work, as part of efforts to prepare them for the Austrian job market.