The vote by the 15-member council was procedural so Russia could not wield its veto.
A resolution convening the General Assembly session was adopted with 11 yes votes. Russia voted no, while China, India and the United Arab Emirates abstained.
The move is the latest in a flurry of diplomacy at the United Nations in New York.
It follows a Russian veto on Friday of a draft council resolution that would have deplored Moscow's invasion of Ukraine. China, India and the United Arab Emirates abstained and the remaining 11 members voted yes.
The General Assembly, which will meet on Monday, is expected to vote on a similar resolution as soon as Wednesday, US Ambassador to the United Nations Linda Thomas-Greenfield told NBC's Meet the Press on Sunday.
No country has a veto in the General Assembly. While the assembly's resolutions are non-binding, they carry political weight.
Action at the United Nations is viewed as a chance to show Russia is isolated because of its invasion of neighbouring Ukraine.
They will be looking to improve on the 100 countries who voted in favour of a General Assembly resolution in March 2014 after Russia annexed Ukraine's Crimea region.
That resolution declared invalid a referendum on the status of Crimea.
The vote will be come at the end of the emergency special session. It will only be the 11th such General Assembly session convened since 1950.
The Security Council is also set to meet again on Monday for a briefing on the humanitarian needs of civilians in Ukraine, requested by France, the United States, Britain, Norway, Albania, Ireland and Mexico.
It will be the fifth meeting of the council on Ukraine in the past week.
Russia would be in a position to block the move if it chooses. It has council veto power along with the United States, France, Britain and China.
