Ms Sturgeon was questioned by police and released without charge as part of an investigation into the SNP’s funding and finances.
The former party leader said she was “innocent of any wrongdoing”.
An SNP spokesman said the party was co-operating fully with the investigation.
The force has been investigating for the past two years what happened to £660,000 of donations given to the SNP by independence activists for use in a future independence referendum campaign.
SNP MP Angus MacNeil joined opposition parties in calling for Ms Sturgeon to be suspended from the party – saying “this soap-opera has gone far enough”.
“Nicola Sturgeon suspended others from the SNP for an awful lot less,” Mr MacNeil tweeted.
Scottish Conservatives chairman Craig Hoy said Mr Yousaf must “now show some leadership and suspend his predecessor from the SNP”.
Ms Sturgeon was taken into custody and questioned by detectives at a police station after she attended voluntarily shortly after 10:00 on Sunday.
Officers had up to 12 hours from the time Ms Sturgeon was arrested before they had to decide whether to charge her with a crime or release her while their enquiries continue.
She was released from custody at about 17:25 on the same day – well before the deadline expired and just over seven hours since her arrest.
Police said a report would be sent to the Crown Office and Procurator Fiscal Service.
Nicola Sturgeon arrested as part of SNP finances investigation – in 80 seconds
The former first minister published a statement on Twitter shortly after police confirmed her release.
She said: “To find myself in the situation I did today 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.”
She went on: “Innocence is not just a presumption I am entitled to in law. I know beyond doubt that I am in fact innocent of any wrongdoing
It follows the arrest of her husband, former SNP chief executive Peter Murrell, on 5 April by officers who searched the couple’s home in Glasgow as part of their Operation Branchform probe.
The SNP’s headquarters in Edinburgh were searched on the same day and a luxury motorhome valued at about £110,000 was also seized by police from outside the home of Mr Murrell’s mother in Dunfermline.
Almost two weeks later, the party’s treasurer Colin Beattie was arrested.
Both men were released pending further investigations, with Mr Beattie resigning as treasurer a short time later.
The arrest of the former first minister had been widely expected as she was one of the three signatories on the SNP’s accounts alongside Mr Murrell and Mr Beattie – although there was no indication of when it was going to happen.
