He said the DUP would speak to the PSNI to seek answers about the killing.
Mr McGuigan was shot at Comber Court in east Belfast on Wednesday night.
Asked if he was concerned about IRA involvement, Mr Robinson said: "I think everyone should be concerned that would be the case."
"Let's allow the police to fully investigate the matter," he said.
"We will speak to the PSNI to see what their findings are in terms of the involvement of any organisation.
"But let's be very clear, there will be repercussions if that was found to be the case."
He added: "It would certainly be totally unacceptable for any organisation which is involved in violence to be part of the Executive of Northern Ireland."
Mr Robinson was referring to the potential political consequences for Sinn FÃ©in, the main republican party in Northern Ireland and the second biggest party in the assembly.
Mr Robinson described the murder as a "savage killing" and said it "should be a warning to all politicians and others about how easy it would be to slip back into those bad old days."
He said there were people who would step into a "void" to "exploit political difficulties".
"The collapse of the assembly will feed that kind of activity we have seen over the last number of weeks from dissidents in our society," the DUP leader added.
Sinn FÃ©in MLA Alex Maskey said he did not believe the PIRA was involved in the murder and expressed concern about "unhelpful speculation".
"I don't accept for one second that the IRA has been involved in this, it just doesn't register at all," he said.
"We will be meeting the PSNI shortly to make sure that they do their job, which is to have a very thorough and rapid, speedy and professional investigation into whoever caused this killing and whoever caused this killing should be and hopefully will be brought to justice as speedily as at all possible.
"We're calling for calm, we're calling for respect for this particular family at this time in the midst of their grief and we're cautioning against unhelpful and unwelcome speculation."
In a separate development, Mr Robinson said there had been talks over the summer between parties about the deadlock over welfare and that they would continue.
He said: "We've gone through the exploratory stage.
"We're now at the preparatory stage where we look at what can be done in the circumstances. But clearly by the autumn it will be necessary to have reached an agreement."
He said he did not want to be "too precise" over the date by which there had to be a resolution, but that the autumn was the critical time.
Mr Robinson added that progress was being made on all of the other issues in the Stormont House Agreement, including new mechanisms to deal with the past and the civil service voluntary exit scheme.
But he said the main issue holding up the process was welfare.
He warned again that the political institutions in Northern Ireland were in danger if the situation was not resolved.
"If Stormont House is not implemented, we are still in the situation where Stormont is not fit for purpose and is capable of collapsing," he said.
First Minister Peter Robinson has said there will be repercussions if it is found that the Provisional IRA was involved in the murder of Kevin McGuigan Sr.