The Prime Minister also refused to comment when asked if he knew before the election that an unnamed MP was being investigated.
Asked by Labour in Parliament when the Police Minister was first told, Mr Woodhouse said despite reports of a police investigation, police had declined to confirm any such investigation to media "and it is not for the Minister to get ahead of police in discussing unconfirmed operational matters." "It is not appropriate, nor in the public interest for me to discuss details relating to whether I may have received or provided details on a specific police matter."
Labour leader Andrew Little said it was unacceptable for the Government to keep stonewalling.
"It's been two weeks since questions started being asked about what they were told and when they knew. They've just refused and refused and refused. That's not acceptable for a Minister of the Crown to act in that way. They are in public office with public information and they should disclose that information when asked."
He said he was surprised if police had withheld the name of the MP from ministers and compared it the former Labour MP Darren Hughes, who resigned in 2011 during a police inquiry from which no charges were laid. "I certainly know in the case of Darren Hughes, the minister seemed to know exactly who was under investigation so it surprises me the police didn't tell them the identity of the MP."
He said it was up to the Police Commissioner to clarify what was revealed.
Speaking to media, Mr Woodhouse again refused to answer when he had found out or whether he had told the Prime Minister. "It is certainly not appropriate for me as Police Minister to talk about things that police aren't prepared to confirm."
He said he was briefed on a range of matters under the no surprises policy. "Matters like that are between the Commissioner and myself. They are confidential and I don't intend to breach those confidences."
Asked why an MP being under investigation in the lead up to an election was not in the public interest, he said police had not confirmed there was an investigation and it was up to them to make comments. He said he was satisfied the no surprises policy was working well "and I'm not prepared to say any more."
A spokesman for police declined to comment on either Mr Woodhouse's statements or the Herald report about the timing of the briefings, citing legal reasons.