“During the pandemic, travel should be kept to an absolute minimum.”
Border patrols will be increased to ensure compliance with travel restrictions.
The interior ministry said that it had been in contact with German Interior Minister Horst Seehofer over the new border measures and that talks with ministers in other countries were to follow.
Austria shares borders with Germany, Switzerland, Liechtenstein, Italy, the Czech Republic, Slovakia, Hungary and Slovenia.
Hotels, restaurants, bars and cafes will not be reopening with the new relaxation of restrictions next week, along sports and leisure facilities, theatres, operas and cinemas.
Austria reported 1,317 new infections on Sunday, bringing the total to 420,644 since the outset of the pandemic. Twenty-two people died, raising the country's total COVID-19 fatalities to 7,906, according to official figures.