The brigades could be based in Murmansk, Arkhangelsk or other areas, Russian news agencies reported.
Anatoly Serdyukov said Russia had studied the specialist Arctic troops in Finland, Norway and Sweden.
The BBC's Daniel Sandford, in Moscow, said Russia's plans to increase the number of troops stationed in the Arctic still seem to be at an early stage though earlier announcements had mentioned only one brigade.
"The General Staff is currently working on plans to create two such units," Mr Serdyukov was quoted as telling media by state news agency Itar-Tass.
He said his ministry was still in the process of working out specifics, such as troops numbers, weapons and bases, but a brigade includes a few thousand soldiers.
Just this week, Mr Putin said that Russia would "expand its presence in the Arctic" and "strongly and persistently" defend its interests.
At the same time he promised to look after the region's vulnerable ecology.
It is believed that there are substantial unexploited reserves of gas and oil under the Arctic Ocean.