Humza Yousaf had admitted it was a "difficult day" for the SNP following the arrest of former chief executive Peter Murrell.
The party's headquarters in Edinburgh were also raided as part of a wider investigation into its finances.
The First Minister was making a planned visit to the new Gorbals Health Centre in Glasgow.
He told Sky News: "My reaction, as you’d imagine, much like anybody involved in the SNP, is that this is a difficulty for the party.
"But, again, I’d just reiterate and emphasise it’s so important for me not to comment on a live police investigation and be seen to prejudice that in any way, shape or form.”
He continued: "I think there’ll be concern from the public but, again, there is a live police investigation under way and we will wait to see what comes at the conclusion of that police investigation."
Yousaf insisted he only became aware of the arrest of Peter Murrell after it took place.
The new SNP leader said he would not criticise the timing of the police investigation.
"I won’t comment on a live police investigation," he said. "Of course, as party leader, I will know the financial state and health of the party.
“As I’ve already made clear, one of the first things I did was talking to our party lawyers around about the current live police investigation.
“I’ve never been an office bearer in the party, I’ve not had a role in the party finances.”
He said the party’s national executive committee had agreed to a review of governance and transparency.
Asked if the arrest would hurt the SNP in the polls or at a potential by-election, he said: “It certainly doesn’t do us any good.
“People will have questions, there will be some concerns. Our party membership will have concerns too.
“What I can commit to as party leader is that we want to be absolutely transparent.”
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