Scotland's former first minister was speaking for the first time since Peter Murrell was questioned over the SNP party's finances.
The former SNP chief executive was arrested and released without charge pending further investigation.
Ms Sturgeon told reporters recent days had been "obviously difficult".
Outside her Glasgow home, which was the subject of a two-day search by Police Scotland, the former party leader said: "Well first off, there is obviously nothing I can say about the ongoing investigation.
"As much as there are things I may want to say, I'm not able to do so, other than to say that, as has been the case, there will continue to be full co-operation.
"The last few days have been obviously difficult, quite traumatic at times, but I understand that is part of a process."
Asked if she had been questioned by officers, Ms Sturgeon replied: "I haven't, but I will fully co-operate with the police as and when they request that, if indeed they do."
She declined to say whether detectives have indicated that they wish to speak to her.
Police searched their home in Glasgow, with uniformed officers also searching the SNP's headquarters in Edinburgh.
She asked for a "little bit of privacy in my own home" following the week's events.
She added: "My neighbours, I think, are also entitled to a wee bit of privacy as well.
"Over the years, as a result of living next door to me, they've been subjected to more than their fair share of disruption and inconvenience.
"And that has obviously been particularly the case over the last couple of days."
Mr Murrell, who has been married to Ms Sturgeon since 2010, resigned as chief executive of the SNP after taking responsibility for misleading statements about a fall in party membership.
Last year it emerged that he gave a loan of more than £100,000 to the SNP to help it out with a "cash flow" issue after the last election.
The party had repaid about half of the money by October of that year.
At the time an SNP spokesman said the loan was a "personal contribution made by the chief executive to assist with cash flow after the Holyrood election".
He said it had been reported in the party's 2021 accounts.
Ms Sturgeon told assembled media: "Peter's at home as you would expect it to be. Peter's not able to say anything.
"Again, that's not necessarily a matter of choice. That's just the nature of this."
Ms Sturgeon's comments follow a tumultuous week for the SNP.
It emerged on Friday that the firm that audits the SNP's finances had resigned.
Accountants Johnston Carmichael had worked with the party for more than a decade but said the decision was taken after a review of its clients.
The BBC understands Johnston Carmichael resigned before Mr Murrell's arrest.
Earlier on Saturday, SNP president Mike Russell conceded the party had been plunged into its biggest crisis in half a century.
Mr Russell also said he does not think independence can be achieved "right now".