Public confidence has been damaged by the incident at the Vulcan Naval Reactor Test Establishment in Dounreay, Caithness, according to shadow defence secretary Vernon Coaker and shadow Scottish secretary Margaret Curran.
UK Defence Secretary Philip Hammond revealed details of a small internal leak of radiation on Thursday as he announced that the nuclear submarine HMS Vanguard is to have its reactor refuelled at a cost of £120 million.
He told the Commons that low levels of radioactivity had been found in the cooling waters of the test reactor at Dounreay in 2012.
Mr Coaker and Ms Curran said there were "significant questions" about the handling of the incident, particularly the two-year delay in making it public.
In a joint letter to MP James Arbuthnot, chair of the Defence Select Committee, they said: "It is critical that the public, particularly those who live close to facilities in Dounreay, have complete confidence in the safety regime that is in place.
"We believe there must be public confidence in the Government to be open and transparent about these issues. This confidence has been damaged by the two- year delay in informing the public.
"There are still many unanswered questions. That is why we are requesting that the Defence Select Committee undertakes an inquiry into the incident at Dounreay.
"We believe such an inquiry would not only shed light on what happened following the incident at Dounreay, but would also help to restore public confidence and trust."
Mr Hammond told MPs that both the independent Defence Nuclear Safety Regulator and the Scottish Environment Protection Agency (Sepa) had been alerted to the problem.
Following the announcement in the Commons, Scottish Veterans Minister Keith Brown accused Westminster of "disrespect" and said it was "'totally unacceptable" that the Scottish Government had not been told.
The joint letter from Mr Coaker and Ms Curran queries "a nine-month delay" in the Ministry of Defence informing regulator Sepa and raises concerns that the Scottish Parliament was not made aware.
It continues: "It is unclear if the MoD informed Sepa under a non-disclosure agreement."
A Ministry of Defence spokesman said: "The Scottish Environment Protection Agency (Sepa) was not ordered to withhold information from the Scottish Government and it is absolutely wrong to suggest otherwise.
"Having been told about the situation, Sepa themselves chose not to inform ministers based on their expert view that the local community and environment is not at risk.
"As we have consistently made clear, the announcement was about the decision to re-fuel HMS Vanguard, not the issue at Dounreay, where regulators judged the reactor continues to operate safely."