The missile shield involves placing a radar system in the Czech Republic and interceptor missiles in Poland - two Eastern European countries that were in formerly in the Soviet bloc during the Cold War era.
China has also expressed concerns at another US shield being built around Japan, intended to ward off potential missile threats from North Korea.
Beijing is concerned that the US might use the same system to shield Taiwan, the self-ruled island that China claims as a renegade province.
Over the weekend Vladimir Putin the Russian president warned that Moscow could take "retaliatory steps" if the European shield is realised.
Such steps, he said, could include aiming nuclear weapons at US military bases in Europe
Russia believes the shield in Eastern Europe is meant for it, and says it has no choice but to boost its own military potential in response.
The US argues the missile shield would easily be defeated by Russia's large military arsenal, saying the network is meant to protect NATO allies against missiles launched from what it calls "rogue states" such as Iran and North Korea.