All opposition deputies boycotted the vote, walking out of the chamber.
Following the vote, Voronin said: "The conditions for dissolving parliament exist."
'Clean and attractive'
Opposition parties had already sought new elections after alleging irregularities in parliamentary elections that were held in April.
The polls descended into violence in the Moldovan capital, in which dozens of people were injured.
The opposition refused to heed a last-minute appeal by Greceanii, who said: "I consider that the most important choice is for national accord and constructive dialogue between all political forces."
Speaking before the vote, Serafim Urechean, the leader of the opposition Our Moldova Alliance, said: "I guarantee you that today will be a day of celebration. The Communists will understand for the first time that people are not for sale ... they will understand that times have changed."
The election of Greceanii, who rose up through the state finance administration to her present post as premier, would have represented a reshuffle among a tight political elite.
Voronin was elected parliament speaker on May 12, giving him considerable influence after he departs the presidency.
Last month, he described Greceanii as "honest, clean and attractive".
Greceanii faced a second token Communist whose presence on the ballot was needed to make the vote valid because the opposition has put no one forward.
The prospect of prolonged instability in the country has prompted concern on the part of the European Union and Russia.