The resolution to sack the government and Strelet, in office only since late July, was backed by 65 lawmakers out of 101, due to the combined vote of three pro-Russia parties.
Moldova has been rocked by a political crisis over a USD 1 billion (910-million-euro) corruption scandal that saw a former prime minister arrested earlier this month amid popular protests.
The country is torn between those who want it to join neighbouring Romania in the European Union and those who want closer relations with Moscow, the Soviet-era master.
Russia maintains troops in Moldova's breakaway Transdniestr area bordering Ukraine.
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Strelet, who leads the Liberal Democratic Party, took office on pledges to strengthen ties with the EU and push ahead with attempts to enter the 28-country bloc.
In his final speech in parliament, he said: "I am seriously worried about the future of the country. I see that some politicians have no desire to maintain the smallest amount of stability."
"They want chaos, that is why they supported the dismissal of the government."
But the leader of the Communist Party, Violeta Ivanov, attacked Strelet's brief stint in power as inept.
"We have the most unprofessional government, the coffers are empty, the banking system is on the brink of collapse," she said.
Strelet's tenure has been dominated by the graft scandal and the alleged role in it of his party's former leader Vlad Filat, who was prime minister from 2009 to 2013.
Filat was detained this month and his assets seized in a probe into the disappearance of a billion dollars from the country's banking system.
"In recent weeks, the prime minister Valeriu Strelet has not been working for the government but has been defending his party leader Vlad Filat," complained the leader of the Democratic Party, Marian Lupu.
With Filat's detention, the pro-European bloc of Strelet lost its parliamentary majority, allowing the vote of no confidence. Moldova's previous prime minister, Chiril Gaburici, quit in June over allegations he faked his high school diploma.