Humza Yousaf has refused to suspend Nicola Sturgeon from the SNP following her arrest yesterday.
The First Minister said his predecessor had been released without charge so would not face losing the party whip.
Speaking to reporters on a visit to Inverness today, Yousaf said he saw "no reason" to suspend Sturgeon.
"I'll not suspend Nicola's membership. I'll treat her in the same way I've treated, for example, Colin Beattie," he told BBC Scotland.
"Those that have been released without charge I see no reason to suspend their membership."
Sturgeon became the third senior Nationalist to be questioned by detectives in connection with Operation Branchform, which is investigating how party donations were spent .
Colin Beattie, the former SNP treasurer, and Peter Murrell, the party's former chief executive, were both quizzed by cops in April but did not face charges.
Sturgeon was released on Sunday evening without charge pending further investigations.
The former SNP leader has denied any wrongdoing and described her arrest as "distressing".
Asked if Sturgeon should resign the whip, Yousaf said today: "There's no pressure on her to do so from the party or from me as leader of the SNP."
He added: "She has been released without charge and I think it is so important that presumption of innocence is upheld."
It comes after two of the party's MSPs called for Sturgeon to lose the party whip following her arrest.
Ash Regan, who stood against Yousaf for the SNP leadership, said: "I think that Nicola should perhaps consider voluntarily resigning her SNP membership until this can be cleared up."
Michelle Thomson, who was previously suspended by Sturgeon over an unconnected matter, said: "The processes set by the SNP under her leadership were clear.
"Some eight years ago when an MP, I was required to resign the SNP whip although I was never personally under investigation and was certainly not arrested."
Scottish Labour leader Anas Sarwar said: “Ultimately, that’s a matter for the SNP, but if you look at previous incidents that are similar, then those individuals have been suspended.
“The question is for Humza Yousaf, is he strong enough to take action? Or is he too weak to take action?
“That’s a decision for them, what I’m more interested in is the fact that we now have an incompetent and dysfunctional SNP Government, a Government now famed for secrecy, for cover-up and economic instability and incompetence.”
Douglas Ross, the Scottish Conservatives leader, branded Yousaf as "weak" for not suspending Sturgeon.
He said: "A weak leader unable to stand up to his predecessor. The SNP should follow their own precedent and suspend Nicola Sturgeon while she is being investigated by the police."
In a statement yesterday, Sturgeon said: "To find myself in the situation I did when I am certain I have committed no offence is both a shock and deeply distressing.
“I know that this ongoing investigation is difficult for people, and I am grateful that so many continue to show faith in me and appreciate that I would never do anything to harm either the SNP or the country.
“Obviously, given the nature of this process, I cannot go into detail.
“However, I do wish to say this, and to do so in the strongest possible terms.
“Innocence is not just a presumption I am entitled do in law. I know beyond doubt that I am in fact innocent of any wrongdoing."
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