Nicola Sturgeon’s husband, Peter Murrell, is understood to have been arrested in connection with an investigation into the funding and finances of the Scottish National Party (SNP).
The former SNP chief executive is in custody and is being questioned by detectives.
Police Scotland said a 58-year-old man was arrested as part of an ongoing investigation.
Officers are also carrying out searches at a number of addresses, the force added.
Police Scotland has been investigating the spending of money which was earmarked for Scottish independence campaigning.
The SNP said in a statement: “Clearly it would not be appropriate to comment on any live police investigation but the SNP have been co-operating fully with this investigation and will continue to do so.
“At its meeting on Saturday, the governing body of the SNP, the NEC, agreed to a review of governance and transparency – that will be taken forward in the coming weeks.”
A spokesperson for the Crown Office and Procurator Fiscal Service said: “COPFS will continue to work with police in this ongoing investigation.
“It is standard practice that any case regarding politicians is dealt with by prosecutors without the involvement of the Law Officers.”
It comes just a week after Humza Yousaf was legally sworn in as Scotland’s sixth first minister – replacing Ms Sturgeon after her shock resignation in February.
Mr Murrell, who married Ms Sturgeon in 2010, stepped down as SNP chief executive during the recent leadership campaign last month after more than two decades in the post.
