"NATO is deeply concerned by threats to the physical safety of Estonian diplomatic staff, including the ambassador, in Moscow," the alliance said in a statement. "These actions are unacceptable, and must be stopped immediately."
The alliance called on Moscow to defuse tension over the Soviet war memorial and graves in Estonia "diplomatically."
On Wednesday pro-Kremlin youth activists in Moscow staged an aggressive protest against Estonia's ambassador over the removal of the World War II memorial from central Tallinn, the Estonian capital.
The dispute comes at a time of already testy relations between Russia and its West European neighbors. Russians regard the Tallinn memorial as a tribute to Soviet sacrifices in fighting Nazi Germany. For many Estonians it is a bitter reminder of decades of postwar Soviet occupation.
Serious rioting, mostly by Estonia's ethnic Russian minority, broke out last week over removal of the statue to a military cemetery.