"Russia's foreign policy doctrine has Cold War elements," he told public broadcaster YLE.
"In many ways we're on the brink of a Cold War."
That warning echoed almost word-for-word an assessment given on the weekend by Mikhail Gorbachev, the Soviet Union's last leader, as he attended the 25th anniversary of the fall of the Berlin Wall.
However, despite reports of increased Russian military activity in the Baltic region, Stubb said that the Nordic country's security situation had not changed significantly.
The country is not a member of NATO but participates in NATO's Partnership for Peace Programme and regional military cooperation with its Nordic neighbours.
Stubb said that Finland would maintain good bilateral relations with Russia but would also join its voice with that of the European Union which has imposed a raft of sanctions on Russia in response to the Ukraine conflict.
He indicated there would be no return to Finland's old policy of accommodation towards its powerful eastern neighbour.
He added that continuing sanctions were the best approach to the Ukraine conflict.
"It's the only way, it's soft but firm, it's the only measure we have and it must be used," he said.
"We must remember that at this moment the Russian economy is sinking, the ruble is weakening, oil prices are coming down and international investors are getting out of Russia.
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