The DUP has said Mrs Robinson is to stand down from public office
The NI Assembly's Committee on Standards and Privileges has begun an official investigation into the conduct of Peter and Iris Robinson.
The committee chairman, Declan O'Loan of the SDLP, said the probe into issues raised by a BBC documentary last week was "clearly in the public interest".
The BBC reported that Iris Robinson obtained £50,000 from developers to help her teenage lover launch a cafe.
She failed to register the money with the authorities at Stormont.
She also failed to tell the Westminster authorities, as required by the law.
The BBC Spotlight programme also reported that the first minister, Mrs Robinson's husband Peter, knew about her financial dealings but did not tell the proper authorities.
The committee said on Monday that it received correspondence from Mr Robinson, requesting that it commence an inquiry into the questions that have been raised.
Mr O'Loan said it would establish whether any breaches of the Assembly's code of conduct had occurred.
Castlereagh Borough Council, where Mrs Robinson sat as councillor, has also launched an investigation.
The cafe that Mrs Robinson's lover set up was based in a Castlereagh council facility and in 2008 the council advertised for expressions of interest in the cafe project.
Only one applicant met the criteria - Kirk McCambley, Mrs Robinson's lover.
The deal was sealed on 28 August 2008 and Iris Robinson was in attendance as the council authorised the signing of the lease.
The laws covering local government state that once Mrs Robinson had a financial interest in the business, she was obliged to declare it at any meeting she attended where it was being considered. She failed to do so.
On Friday, the council said the acting chief executive had been instructed to instigate a full investigation.
"In the interests of good governance, the council will keep the local government auditor fully informed of this process," a statement added.