The proposed ban, which would be the first of its kind in Scandinavia, will include the niqab and burqas, as well as masks and balaclavas which will be outlawed in nurseries, schools and universities.
However, the hijab and skullcaps will continue to be worn.
The proposed bill received cross-party support and is expected to come into effect in 2018.
Minister of Education and Research, Torbjorn Roe Isaksen, said in a statement: “These clothes prevent good communication, which is important for students to receive a good education.”
The Interim Minister of Immigration and Integration, Per Sandberg, said being able to communicate with one another was a “fundamental value”.
Local authorities in Norway currently have the power to outlaw the niqab but there is currently no national policy in place.