Mr Murrell, who resigned as the SNP’s chief executive last month, was released without charge on Wednesday evening as police continued an investigation into the SNP’s finances.

The former first minister was scheduled to take part in a discussion about the climate crisis with Patricia Espinosa, a Mexican diplomat who served as the executive secretary of the United Nations Framework Convention on Climate Change from 2016 to 2022.

However, a spokeswoman for Ms Sturgeon confirmed she had now pulled out and would be replaced by Màiri McAllan, the SNP Cabinet secretary for net zero and just transition.

Former first minister Nicola Sturgeon. Picture: PA

The spokeswoman said: “In order to keep the focus of this event on the critical issue of the climate emergency and Ambassador Patricia Espinosa's contribution, Nicola Sturgeon has made the decision not to participate this evening. She is grateful to the festival and Ambassador Espinosa for their understanding, and to Màiri McAllan for taking her place.”

Mr Murrell, who married Ms Sturgeon in 2010, was arrested on Wednesday morning in connection to a long-running Police Scotland investigation into the spending of about £600,000, which was earmarked for Scottish independence campaigning. He was released from custody on Wednesday evening “pending further investigation”.

On Wednesday, a Police Scotland spokesperson said: “A 58-year-old man who was arrested as a suspect earlier today in connection with the ongoing investigation into the funding and finances of the Scottish National Party, has been released without charge pending further investigation.

“The man was questioned by Police Scotland detectives after he was arrested at 7.45am. He was released from custody at 6.57pm.

“Officers also carried out searches today at a number of addresses as part of the investigation. A report will be sent to the Crown Office and Procurator Fiscal Service.

“The matter remains active for the purposes of the Contempt of Court Act 1981 and the public are therefore advised to exercise caution if discussing it on social media. As the investigation is ongoing we are unable to comment further.”

The update came after a spokesperson for Ms Sturgeon said she would “fully co-operate if required” with police following her husband’s arrest.

Ms Sturgeon, who unexpectedly announced her resignation as first minister on February 15, stressed she had “no prior knowledge of Police Scotland’s action or intentions”.

In a statement, a spokesperson said: “It would not be appropriate to comment on a live police investigation. Nicola Sturgeon had no prior knowledge of Police Scotland’s action or intentions. Ms Sturgeon will fully co-operate with Police Scotland if required, however at this time no such request has been made.”

Police have been searching the couple’s house in Glasgow and the SNP’s headquarters in Edinburgh.

First Minister Humza Yousaf, who took over from Ms Sturgeon last week, said the arrest marked a “difficult day” for the party.

An Edinburgh Science Festival spokeswoman said: “While Nicola Sturgeon MSP is no longer attending our Climate of Change event, we are thrilled to be welcoming MSP Màiri McAllan, Cabinet secretary for net zero and just transition who will join Ambassador Patricia Espinosa for this vital conversation.

“The Edinburgh Science Festival has been proudly programming events such as these which highlight and inspire people of all ages and all backgrounds to action on our climate emergency for many years. We look forward to welcoming our audiences to this insightful and inspiring discussion.”

Nicola Sturgeon pulls out of festival event after husband Peter Murrell's arrest