Mr Orpo made the announcement during a news conference on Tuesday.
Finland had only one border checkpoint open, located in the Arctic, after the government closed seven others because of a surge in arrivals of migrants from the Middle East and Africa.
Finland accuses Moscow of ushering the migrants toward the Finnish border.
Authorities say about 900 migrants crossed the border from Russia this month, significantly more than normal. It has accused Russia of trying to create a migration crisis in Finland following the Nordic nation's entry into Nato this year.
Interior Minister Mari Rantanen said the last border crossing for vehicle traffic that remains open, Raja-Jooseppi in Finland's Arctic north, would close at midnight Wednesday.
A railway crossing between the two countries remains open but for cargo traffic only.