Assembly speaker William Hay told surprised politicians in the chamber that current enterprise minister Arlene Foster had been asked to temporarily take on the functions of First Minister.
Stormont officials said the procedural device could last for six weeks.
Read Ken Reid's blog: A strange day
Mr Robinson, who vehemently denies any knowledge of his wife's irregular financial affairs, remains leader of the DUP.
"I continue to contend I have acted ethically and it is particularly painful at this time of great personal trauma that I have to defend myself from an unfounded and mischievous allegation", he said in a statement.
"I count it a great honour and privilege to lead the Democratic Unionist Party and I will continue to do so with the full support of my colleagues," he added.
The first couple have been plunged into crisis after it emerged that Mrs Robinson had secured £50,000 from two wealthy developers to help her then 19-year-old lover Kirk McCambley set up a restaurant business in south Belfast.
A BBC documentary further alleged that her husband became aware of the situation but did not take steps to alert the appropriate authorities.
The Assembly's Committee on Standards and Privileges confirmed it has initiated an official investigation into the conduct of Iris and Peter Robinson.
Sinn Fein Chief Whip Carál Ní Chuilín said the full examination had to be carried out as a "matter of urgency".
Acting First Minister Mrs Foster said solicitors in the Office of the First and Deputy First Minister had already indicated that Mr Robinson did not break any rules.
"On behalf of the First Minister, I want to make it clear that he entirely rejects the sole allegation made by the BBC Spotlight programme and will be seeking to clear his name in the days that lie ahead," the Fermanagh and South Tyrone member said.
"I am personally confident, my party is very confident, that this will confirm that Peter Robinson, the First Minister, acted entirely properly at all times - but let's have this (investigation) and let's have it quickly," she added.
The shock move came just one hour after DUP colleagues backed the beleaguered Mr Robinson, who is under pressure to resign over the scandal.
Deputy leader Nigel Dodds, flanked by party faithful including former leader the Rev Ian Paisley, said they offered Mr Robinson their "wholehearted support" as leader and as First Minister.
Reactions
Sinn Fein, who want policing and justice powers devolved as soon as possible, believe the crisis which existed at Stormont before Christmas has now deepened.
"If you have a political vacuum, it's the history of Ireland that others will step in that vacuum. We need to make sure there's no space," Gerry Kelly told UTV.
UUP leader Sir Reg Empey questioned the appointment of Arlene Foster as a "caretaker" First Minister.
"At this crucial time in the political process, we now have two lame-duck First Ministers, neither of whom can make the decisions necessary to ensure proper, working devolution," he said.
"In a highly cynical fashion the DUP have decided to put party before country.
The SDLP's Mark Durkan said he felt it would be difficult for Mr Robinson to return to the top post.
"Now he has seen reason to move it is hard to see how he can come back and if he does he will certainly be diminished," he said.
"But Peter Robinson's decision to step aside will not do away with the need for further inquiries."
TUV leader Jim Allister said the DUP were preparing a soft landing for Mr Robinson.
"His immediate stepping aside as First Minister may well be a precursor to his departure as DUP Leader at a moment more of his own choosing", he said.
If Mr Robinson resigns, the posts of First Minister and Deputy First Minister, held by Martin McGuinness, would have to be filled, throwing the future of Northern Ireland's power-sharing Executive into question.
Sinn Fein could delay nominating unless the DUP agreed to a timescale for the devolution of policing and justice.
If the power vacuum is not resolved within seven days it would fall to Secretary of State Shaun Woodward to call a Northern Ireland election.
After speaking to Mrs Foster on Monday night, Gordon Brown appealed to the the province's politicians to concentrate on resolving the outstanding political issues facing them.
"I urge all politicians in Northern Ireland, whatever the turbulence of recent events, to remain focused on the business of government, and to recognise the crucial importance of intensifying engagement in those issues which remain to be solved," he said.
Mrs Robinson announced over Christmas that she was quitting politics because of severe depression. She will now stand down sooner than planned as an MP, MLA and local councillor. Her DUP membership of the party was also terminated.
Mr Robinson confirmed his wife is continuing to receive acute psychiatric treatment through the Belfast Health and Social Care Trust.
"As a father and a husband, I need to devote time to deal with family matters," he said.