Scottish First Minister Humza Yousaf has said he "sees no reason" to suspend his predecessor from the Scottish National Party (SNP) despite her arrest yesterday.
Ms Sturgeon later said in a post online she was innocent of any wrongdoing.
But speaking to the BBC today, Mr Yousaf said he would not be suspending Ms Sturgeon from the party and would treat her the same as former treasurer Colin Beattie, and former chief executive - Ms Sturgeon's husband - Peter Murrell, who were also arrested and released without charge in relation to the probe.
"I will do what I believe is right to the values of natural justice," he said.
"Nicola Sturgeon, like Colin Beattie, like Peter Murrell, was released without charge.
"Therefore, I see no reason for their membership to be suspended."
With SNP parliamentarians calling on Ms Sturgeon to resign the whip, however, Mr Yousaf added: "There is no pressure on her to do so from me or the SNP."
In the hours after the arrest, Mr Yousaf, who took over the helm of the SNP in March, has come under pressure to suspend his predecessor until the end of the investigation.
SNP MSP Michelle Thomson suggested Ms Sturgeon should resign the party whip - saying she had had to do this when she was an MP despite not being "personally under investigation" and "certainly not arrested".
Ms Thomson stressed she was a "strong believer in natural justice", including the presumption of innocence until proven guilty in court.
But speaking about Ms Sturgeon said: "The processes set up 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.
"After careful consideration, I feel the right thing for the former first minister to do is to resign the SNP whip," Ms Thomson said.
"This is not because she doesn't deserve to be treated as innocent until proven guilty, she does, but because her values should be consistent."
Former leadership candidate Ash Regan said Ms Sturgeon should consider resigning from the party.
"I think that Nicola should perhaps consider voluntarily resigning her SNP membership until this can be cleared up."
Quitting would "reaffirm (Ms Sturgeon's) commitment to the principles of the party", she added.
Asked if Ms Sturgeon should be suspended from the party, Ms Regan said her successor as SNP leader and First Minister, Mr Yousaf, may already be considering such a move, adding: "Accountability in these types of situations is really important."
"I think he should consider (suspending her)," she told the Good Morning Scotland radio programme.
"I would caveat that, and I think she no doubt will be considering whether she should resign from the party at the moment."
Operation Branchform - the name of the police investigation into the party's finances - has also resulted in the arrests of former SNP chief executive - Ms Sturgeon's husband - Peter Murrell as well as the party's then treasurer Colin Beattie.
Both men were also released without charge pending further investigation.
Following Mr Murrell's arrest, officers searched the home in Uddingston, South Lanarkshire, that he shares with Ms Sturgeon, setting up a police tent in their front garden, as well as the party's Edinburgh headquarters.
No such search was conducted on the home following Ms Sturgeon's arrest and there were no obvious signs of activity at the home this morning.
Mr Murrell has long faced questions over the alleged diversion of £600,000 (€700,000) in SNP donations that were meant to support its drive for Scottish independence.
He also failed to declare a personal loan to the party of more than £100,000 (€116,000).
Ms Sturgeon, 52, in February announced her resignation after more than eight years as Scotland's first minister, saying that she lacked the "energy" to carry on.
Additional reporting: AFP
