Mr Sogavare lost the vote 27 to 23.
Yesterday's vote in Honiara was triggered by a series of defections from Mr Sogavare's coalition government late last month.
The vote followed an arduous debate that stretched over six hours.
Supporters of the motion said MPs had lost confidence in the prime minister because he was not listening to them any more, while development was stalling around the country.
Mr Sogavare's supporters urged MPs to let him finish the final ten months of his four-year term in office.