Mr Gaetjens said the inquiry had been suspended based on advice from the Australian Federal Police.
"This is to ensure that there is no real or perceived intersection between my administrative inquiry and the criminal investigation into Ms Higgins' allegations," he told the hearing.
"Both the (AFP) commissioner and I are concerned that we do nothing that could prejudice the outcome of the police investigation."
Mr Morrison had tasked Mr Gaetjens with conducting the inquiry to investigate whether his office was told about the alleged rape over contradictory claims about when some of his staff knew.
Mr Gaetjens said he had notified Mr Morrison the inquiry would be paused.
“On the 9th of March, because of the commissioner’s advice, I emailed the prime minister’s office staff to tell them I would not be completing the documentation,” he told the hearing.
"And at that same time I also told the Prime Minister of that, just in case his staff asked him any questions as to what was going on."
Mr Morrison had not provided an update reflecting the inquiry had been paused, despite being questioned about the matter in Question Time last week.
Mr Gaetjens would not answer questions pertaining to records of interviews with staff later saying this was for the “benefit of Ms Higgins”.
“I don’t want to compromise that police investigation,” Mr Gaetjens said.
The response sparked backlash from Labor and Greens senators, with Labor frontbencher Penny Wong accusing Mr Gaetjens of attempting to use Ms Higgins as a shield.
"Please don't use her interests as a shield, Mr Gaetjens," Senator Wong said.
AFP Commissioner Reece Kershaw earlier told a separate hearing he held concerns that the inquiry into the rape allegation could hamper the police investigation.
However, Mr Kershaw insisted he had not directly asked Mr Gaetjens to suspend the inquiry but rather informed him about concerns about the possible “intersection” of their investigations.
“My view is that’s a matter for him... to my knowledge I don’t have access to that material so that is a matter for the secretary,” he told the estimates hearing.
Mr Kershaw said the allegation made by Ms Higgins was serious and being pursued by the AFP through its ACT policing arm.
Ms Higgins has reactivated a complaint with police over allegations she was raped in a ministerial office inside Parliament House in March 2019.
In a separate hearing on Monday, Senate President Scott Ryan repeatedly refused to answer questions relating to Ms Higgins’ allegation on grounds it could “complicate” active police investigations.
In response, Labor senators vented frustration at the resistance to provide answers saying the response looked like a “cover-up”.
“It looks like a cover-up Mr President - that's what it looks like,” Labor Senator Katy Gallagher said.
Mr Ryan said he was “conscious” of that but would not respond to questions that risked compromising the police investigation.
“Even if it was easier to answer specific questions - if that was to have the impact of complicating an investigation - I don't think it appropriate,” he said.
Labor and Greens Senators had attempted to ask questions about responses made in the aftermath of the alleged incident involving Ms Higgins.
“I simply am not going to put at risk any police investigation or activities underway for a grave matter like this,” Senator Ryan said.