He would not say which staff member the investigation was related to.
"It's not fair on the complainant and it's not fair on the person who's been complained about," Gribben said.
He confirmed that the staff member was still carrying out their duties as normal during the investigation.
Richard Dellabarca, chief executive of the fund since 2016, did not respond to a request for comment.
NZVIF was established in 2002 in a bid to boost investment in early stage companies and help foster a stronger venture capital market in New Zealand.
Over the next 16 years it invested $173m in 239 New Zealand companies.
At the start of March, a string of Cabinet ministers celebrated a new structure for the fund, which saw the Government direct the New Zealand Superannuation Fund to put $240 million into a new fund - Elevate NZ Venture Fund - which would be managed by New Zealand Growth Capital Partners, which was also contributing $60m to the fund.
The Super Fund, which manages tens of billions of dollars on behalf of taxpayers to cover New Zealand's future superannuation fund needs, refused to say when it first learned of the complaint.
"We are aware of an investigation being carried out on behalf of the Board of NZ Growth Capital Partners. It is awaiting the outcome of that investigation and we cannot comment until it is completed," a spokesman said.
Economic Development Minister Phil Twyford refused to comment on an "employment matter" being dealt with by the fund's board. He was advised about the investigation on March 11.