The South of Scotland MSP asked the Scottish Parliament's Presiding Officer to consider whether she had breached rules when she claimed £1750 in expenses for employing a photographer, Jane McLachlan, for 10 days' work.
She had an affair with the photographer's husband, Mark McLachlan, before she became an MSP.
She repaid the money on October 18, 2012, which, Mrs McLachlan told a newspaper yesterday, was five days after she discovered the affair and threatened to expose it to the press.
Mrs McLachlan also said the photography work - which had been paid for in advance - had never been completed and accused the MSP of trying to "cover her tracks".
Yesterday Labour peer Lord Foulkes said Ms McAlpine should step down as Mr Salmond's parliamentary liaison officer, a role linking the First Minister with party backbenchers.
He said: "It would now be inappropriate for Miss McAlpine to continue."
Holyrood officials said an investigation would be launched and a report prepared for the govering corporate body (SPCB).
A Scottish Parliament spokesman said: "Following Ms McAlpine's request to the Presiding Officer, parliamentary officials will examine whether a claim made by the Member in 2012 was compliant with the Parliament's expenses scheme.
"A full report on the investigations will be made to the Scottish Parliamentary Corporate Body and it will be for the SPCB to determine whether the claim was made in accordance with the principles of the scheme."
An SNP spokesman said: "Joan referred the matter herself to the Presiding Officer, and we are confident that no breach of the rules has taken place. The matter will be addressed according to proper procedure in Scotland - not by preposterous calls from an unelected Lord at Westminster."