The Latvian Defense Ministry said the decision to stay away from the Balex Delta exercise, due to take place on August 26-28 in the Kaliningrad region, had been caused by "a change of NATO's general priorities."
Relations between Russia and NATO soured following Russia's military operation in Georgia.
Earlier, a number of Western countries announced their refusal to participate in joint exercises with Russia, while Moscow said it would not allow a U.S. warship to call at a port on the Far Eastern Kamchatka Peninsula.
The United States refused to let a Russian ship participate in NATO's Operation Active Endeavor naval antiterrorism exercise.
Russia's NATO envoy announced Thursday that the Russian Defense Ministry was temporarily suspending military cooperation with NATO until a political decision on relations had been made.
NATO foreign ministers said after talks last Tuesday that the alliance was freezing contacts with Russia until it pulled its troops out of Georgia, but stopped short of stronger measures.