"This is a very provocative action that cannot go without answer," he said.
Rogozin called the expulsions an attempt to disrupt efforts to improve Russia's relations with the United States.
Nato did not give any official statement, saying the alliance does not comment on intelligence matters.
In February, an Estonian court convicted Simm, who was previously employed at the Estonian defence ministry, of treason for passing over 2,000 pages of domestic and Nato secrets to Russia.
The case caused deep concern at Nato and was highly embarrassing for Estonia.
Estonian media said that information Simm passed to the Russians included documents relating to foreign countries' and international organisations' communication and information systems, data security, intelligence, counter-intelligence and defence policy.
The two Russians were attached to the mission Russia has at Nato's headquarters although it is not a member of the military alliance.
The alliance froze links with Russia after Moscow's military offensive on neighbouring Georgia in August last year.
Russia regards improving relations with Nato as part of a broader effort to improve relations with the West, and in particular with the United States.