Murrell, the estranged husband of former first minister Nicola Sturgeon, stepped down as SNP chief executive in 2023 after more than two decades in the role.
He was arrested that year as part of Operation Branchform, a police investigation into SNP finances.
Murrell was charged with embezzlement in April 2024.
He is accused of embezzling £459,000 from the party between August 2010 and January 2023.
Details of a charge against him – including the illicit purchase of luxury goods, two cars and a motorhome, using party funds – were first reported in the media last week.
Murrell had been expected to appear at the High Court in Glasgow for the preliminary hearing on Friday, but it has been postponed to 25 May at the High Court in Edinburgh.
The request to defer was made by Murrell’s defence team and the Crown in a joint application to the court on the basis that both wanted more time to prepare, according to the Scottish Courts and Tribunals Service (SCTS).
In her statement to parliament, Bain did not refer to the Crown requesting deferral.
She told MSPs: “I understand from media reports that Mr Murrell’s legal representatives sought for the date to be changed and this was agreed by the independent judge sitting in the independent court.”
A SCTS spokesperson told BBC Scotland News it was “very common” for such hearings to be deferred in this manner, especially in complex cases.
The spokesperson added that the decision had been taken independently by the judge, Lord Young, and was not the result of political pressure.
The Scottish government also insisted it had no involvement in the decision to push back the hearing.
It will now take place after the Holyrood election on 7 May.