Stewart Hosie and Angus MacNeil are both reported to have had affairs with journalist Serena Cowdy.
Mr Carlaw said he had written to the Parliamentary Standards Commissioner.
First Minister Nicola Sturgeon told the BBC she had seen no evidence of any breach of parliamentary expenses rules.
But Ms Sturgeon, who is also the SNP leader, said it was for the watchdog to decide. She also said that "even politicians have a right to privacy".
Labour MP Graham Jones is understood to have made a separate complaint about Mr MacNeil and Mr Hosie to a second watchdog, the Independent Parliamentary Standards Authority (Ipsa).
Mr MacNeil is said to have stayed with Ms Cowdy at the Park Plaza hotel in London, and then claimed for the room on expenses.
Ms Cowdy is reported to have later been involved in a relationship with SNP deputy leader Mr Hosie, who recently separated from his wife, SNP MSP Shona Robison.
Mr Carlaw, the Scottish Conservative deputy leader, wrote to the standards commissioner, Kathryn Hudson, saying "it has been alleged in several media reports" that Mr MacNeil and Mr Hosie had "conducted their respective affairs in either accommodation or hotels paid for by the taxpayer".
He said this would break rules which say members should only use expenses "in support of parliamentary duties", and nothing that could "cause significant damage to the reputation and integrity of the House of Commons".
In response, the SNP said: "The expenses were approved by the Commons authorities in line with the rules on MP's London accommodation, and none of them involved any additional cost to the public purse beyond that.
"This is the height of hypocrisy from the Tories, given the extent of flagrant abuse of expenses by their MPs which has been exposed in recent years - they simply don't have a leg to stand on when it come to this issue."
Prime Minister David Cameron also made a veiled reference to the allegations in the House of Commons, when he said: "I know the SNP have got other things on their mind - I think actually it's mostly the same thing on their minds."
Questions about the use of hotel accommodation have chiefly focused on Mr MacNeil.
The MP for Na h-Eileanan an Iar (Western Isles) has claimed about Â£90,000 in accommodation expenses since 2010/11, including Â£17,823.97 in 2014/15 - the period in which he was said to have been having an affair with Ms Cowdy.
The vast majority of the claims have been for hotels in the London area.
This is despite Mr MacNeil owning a flat in Lambeth, which is about a 15-minute walk from the House of Commons.
Mr MacNeil, who separated from his wife last year, is understood to have bought the flat under previous Westminster expenses rules, which allowed him to charge mortgage interest payments to his parliamentary expenses.
But when the rules changed following the MPs' expenses scandal, Mr MacNeil became one of several MPs who chose to rent out their properties and instead claim expenses for staying in hotels or rented accommodation when in London.
There is no suggestion that the practice is against Westminster expenses rules, and MPs do not have to disclose details of any guests to the authorities.
Mr MacNeil had previously said that MPs should be allowed to claim for flats they own, as they did in the past.
Responding to the latest allegations, he said: "My accommodation in London is claimed under normal expenses, as is the case for all MPs, and the cost of this is compliant with the rules of the Independent Parliamentary Standards Authority (IPSA).
"I don't like to comment on my personal life or related tabloid stories, but my marriage sadly ended for very different reasons to what has been suggested in lurid newspaper stories this week.
"For the record, as if I even need to say, I have never had so much as a crossed word with my colleague Stewart Hosie MP."
Mr MacNeil criticised the "awful personal invasion where tabloids treat you like a commodity disregarding effects on children especially".
The MP added that he was thankful for the support he had received "in the constituency, wider Scotland and at Westminster including MPs from across the political spectrum".
He said: "It has been a challenging week in which I am continuing to do my job and keep appointments as planned."
Mr MacNeil was previously forced to pay back almost Â£900 in hotel expenses after exceeding the nightly rate set out under Independent Parliamentary Standards Authority (Ipsa) rules.
Allegations of Ms Cowdy's affairs with the two SNP MPs have dominated the front pages of Scotland's newspapers over the past two days.
SNP leader Nicola Sturgeon - who was re-elected as Scotland's first minister on Tuesday - said marriages and relationships ran into problems "for all sorts of reasons", and said "even politicians have a right to privacy".
She said: "I've seen no evidence of any breach of parliamentary expenses rules, but ultimately of course that's a matter for the parliamentary authorities to determine.
"Beyond that, these are matters that are private and personal matters. Now I accept politicians will always be under heightened scrutiny but even politicians have a right to a private life."
The first minister was photographed in the Holyrood chamber embracing Ms Robison - who served as her health secretary until the recent election, and who has been married to Dundee East MP Mr Hosie for nearly 20 years.
Tory MSP Jackson Carlaw is to report two SNP MPs to a Westminster watchdog over allegations they claimed expenses for accommodation while carrying out extra-marital affairs.