The resolution, adopted 64-15 with 83 abstentions, urges Russia to complete "unconditionally and without further delay" an orderly withdrawal of its troops and armaments from the breakaway Transdniester region of Moldova.
The stationing of foreign military forces on the territory of Moldova without its consent violates its sovereignty and territorial integrity, said the resolution.
The problem must be resolved in good faith, unconditionally, without further delay and in a peaceful manner, it said.
The Russian troops, known as the Operational Group of Russian Forces, remain in Transdniester guarding the Soviet-era arms depots, although Russia pledged to withdraw them in 1999.
The General Assembly resolution noted that the Operational Group of Russian Forces are not part of a tripartite peacekeeping mission in Transdniester established under a 1992 cease-fire agreement.
Russian Deputy Ambassador Dmitry Polyanskiy said that the vote at the UN assembly undermined bids by the Organization for Security and Cooperation in Europe (OSCE) to settle the conflict in Moldova.
Pro-Russian separatists in Transdniester declared independence from Moldova in 1990. In 1992, the separatists fought a war against government forces. With the 1992 cease-fire agreement, the conflict is considered "frozen."
The non-binding General Assembly resolution decides to include the issue of Russian withdrawal in the provisional agenda of its next annual session that starts in September 2018.