Yousaf's resignation on Monday came just 13 months after he replaced Nicola Sturgeon as Scotland's leader, and sparks another leadership contest in the Scottish National Party.
The crisis in the SNP gives an opportunity for the United Kingdom opposition Labour Party to regain ground ahead of a national election expected this year.
The motion of no confidence in the government was submitted by Scottish Labour last week, after Yousaf said he was ending a coalition with the Scottish Green Party.
Scottish parliament listings showed the vote was scheduled for Wednesday.
Facing a separate vote of no confidence in his own position as first minister, Yousaf said he would step down as Scotland's leader as opposition parties including the Greens lined up to vote against him.
That vote now will not take place.
However, Labour's wider motion of no confidence in the whole government is set to be opposed by the Greens, meaning that it will likely fail and the SNP will have chance to form a new minority government under another leader.
Former leader John Swinney has said he is considering standing while Yousaf's former leadership rival Kate Forbes is seen as a possible candidate.
If the Labour no confidence motion were to be passed, it would result in the resignation of the government and likely Scottish elections thereafter.
Scottish Labour leader Anas Sarwar said it would be a democratic outrage for the SNP to choose another leader - and thus First Minister - without a parliamentary election.
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