The treaty places limits on the number of conventional weapons that can be deployed west of the Ural Mountains.
President Vladimir Putin called for the suspension because NATO countries have not ratified a revised version of the treaty, which originally was signed in 1990.
Russia "is prepared for continuing a results-oriented dialogue on the CFE during its suspension," a ministry statement said.
The Organization for Security and Cooperation in Europe urged Russia to reconsider the moratorium.
"The loss of the [treaty's] system of limitations, information and verification would be detrimental to all and could have security implications for all of Europe," said Spanish Foreign Minister Miguel Angel Moratinos, the OSCE chairman.
A senior Russian military official said two mountain brigades had been deployed in the North Caucasus, "outside the flanking limitations stipulated by the CFE," Interfax reported. The brigades were deployed in Dagestan and Karachayevo-Cherkessia, Interfax said.
NATO members said Wednesday that they "deeply regret" the long-expected decision but would continue to meet their obligations under the treaty. "NATO allies ... want to resolve the current impasse and preserve the benefits of this landmark treaty," NATO said in a statement. "They have therefore chosen not to respond in kind at this stage."
NATO allies would meet treaty obligations regarding exchange of military information at a scheduled meeting in Vienna on Friday, the statement said. Russia is widely expected to skip the meeting.
Analysts doubt that the suspension will spark a new arms race and see it as Moscow's way of registering discontent over NATO's eastward expansion. The NATO statement appealed to Russia to rescind its decision and to respond to proposals put forward by allies, notably the United States, aimed at resolving the standoff. "NATO allies strongly urge the Russian Federation to respond to these efforts," it said.
The original treaty was a key agreement of the late Cold War era, and the 1999 revision was aimed at reflecting the shift in the military power balance after the collapse of the Soviet Union. Russia ratified the updated treaty in 2004, but the United States and other NATO members have refused to follow suit, saying Moscow first must fulfill obligations to withdraw forces from Georgia and from Moldova's separatist region of Transdnestr.
Putin's call for a temporary suspension of the treaty coincided with mounting anger in the Kremlin over U.S. plans to build a missile defense system in Eastern Europe.
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