The former first minister was quizzed by detectives for seven hours before being released without charge.
Police Scotland have launched an investigation into the whereabouts of £660,000 donated to the SNP for a second independence referendum campaign
Following her release this evening, Sturgeon issued a statement on Twitter in which she said it was “beyond doubt” that she was innocent.
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.”
Ms Sturgeon went on: “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 to in law. I know beyond doubt that I am in fact innocent of any wrongdoing.”
Sturgeon thanked “the many people who have sent messages of support over these past difficult weeks – including since today’s news broke”.
She added: “Thank you also to my close circle of family and friends who are giving me much-needed strength at this time.”
Police Scotland are investigating claims that the donations from activists to support the campaign for a second independence referendum were used for other purposes.
The inquiry was launched following allegations that the money, which was meant to be in a ring-fenced fund, had been misappropriated.
An SNP spokesperson said: “These issues are subject to a live police investigation.
“The SNP have been co-operating fully with this investigation and will continue to do so, however it is not appropriate to publicly address any issues while that investigation is ongoing.”