Moscow was "weaponising misinformation" in a bid to expand its influence and destabilise Western governments and weaken Nato, he said.
Vladimir Putin had chosen to become a "strategic competitor" of the West.
Sir Michael said it was vital alliance members strengthened cyber defences.
His speech, at the University of St Andrews, came hours before Theresa May was due to use an informal summit in Malta to press EU Nato members to boost defence spending.