John Swinney said he was "stunned" by Mr Carlaw's sudden resignation, and wished him well for the future.
The Deputy First Minister told BBC Radio Scotland: "I had absolutely no inclination this was coming.
"Leadership is tough, and his statement is very personal reflection on his own assessment of his position. I can't imagine it has been an easy conclusion for him to come to."
READ MORE: Jackson Carlaw resigns as leader of the Scottish Conservatives
Tory MP Douglas Ross is expected to take on the role.
READ MORE: Douglas Ross rumoured to take over as Jackson Carlaw quits
Carlaw concluded he is not the best person to make the case for Scotland staying in the Union.
In a statement, he said: "Over the summer I have had the chance to think hard about my role as leader of the Scottish Conservatives.
"Nothing is more important to me than making the case for Scotland's place in the United Kingdom.
“I believe the Scottish Conservative and Unionist party is the most important voice in Scotland for setting out that positive argument. I am clear that nothing must get in the way of doing so.
"In the last few weeks, I have reached a simple if painful conclusion – that I am not, in the present circumstances, the person best placed to lead that case over these next vital months in Scottish politics prior to the Holyrood elections. Given the importance I attach to the job, I've therefore decided to stand down with immediate effect."
Carlaw added: “It is not an easy call but I have spent a lifetime in politics holding to the maxim that party and country comes first. I believe I am doing my duty by holding to that view now.
“I simply believe that a new leader will be able, as we recover from the Covid emergency, to make the case for the Scottish Conservatives and the Union better than me. That is all that matters."
Responding to the announcement, Boris Johnson thanked Carlaw.
He commented: “Jackson Carlaw has been a tremendous servant to the Scottish Conservative Party for more than four decades.
“As an activist, deputy chairman, deputy leader and leader, he has given his all and deserves our thanks for his efforts.
“It is a mark of his commitment to the cause that he chooses to stand aside at this time and I offer my best wishes to him, Wynne and the family.”
READ MORE: This is Boris Johnson's response to Jackson Carlaw quitting
Nicola Sturgeon sent her best wishes to the outgoing Scottish Tory leader.
"I wish Jackson Carlaw all the best. We’ve crossed swords politically on many occasions, but worked constructively on some issues too – he has, eg, been a strong voice for women suffering mesh complications. Leadership is a tough business and I’m sure his decision wasn’t easy."
READ MORE: 'We’ve crossed swords politically': FM reacts to Jackson Carlaw quitting
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