Frank-Walter Steinmeier told news website Spiegel Online that Putin's announcement was "unnecessary and certainly not a contribution to stability and detente in Europe".
He said the world had changed since the end of the Cold War "but the old reflexes from this time are apparently more alive than we thought even last year".
"I can only warn against giving in to such reflexes and entering into an accelerated spiral of escalation in word and then deed," Steinmeier said.
Putin on Tuesday rattled the West by saying that Russia would add more than 40 new intercontinental ballistic missiles to its nuclear arsenal this year.
Russia and the West are currently locked in their worst standoff since the collapse of the Soviet Union because of the conflict in Ukraine.
Moscow has lashed out at reported US plans to deploy heavy weapons to its jittery NATO allies in eastern Europe, with Putin saying that the US-led alliance is "coming to our borders".
Steinmeier said both sides would be ill-advised to enter into a Cold War-style arms race.
"We must make sure that we, so soon after the emergence of the Ukraine crisis, do not tear down the European peace that we built with so much effort and care after the fall of the Berlin Wall," he said.