The fund, which invests Norway's oil and gas revenues, bought a $1.6 billion (£1b) stake in motor racing's Formula One in May 2012, together with investors BlackRock and Waddell & Reed.
The call by politicians comes after the newspaper Dagens Naeringsliv questioned whether the fund violated its mandate by making the deal. The fund can only buy a stake in an unlisted company if the company plans an initial public offering. After the deal was made, a planned Formula One IPO was cancelled.
"The report brings a need to clarify under which conditions the fund can invest in companies with unlisted shares," Hans Olav Syversen, the head of the Norwegian parliament's finance committee, told Reuters.
He said he would question the head of the fund and the central bank about the deal during a parliamentary hearing due in coming weeks.
Another member of the finance committee said he was seeking a response from the finance ministry about the acquisition.
"I have sent a written question to the finance minister on this question and she has six days to reply," Terje Breivik, the finance spokesman for the Liberals, told Reuters. "The way it is reported in the media, this suggests that this was at the very limit of what the fund is allowed to do."
Syversen is a Christian Democrat and Breivik a Liberals. Their parties are key supporters in parliament of the minority government of Prime Minister Erna Solberg.
Parliamentarians are currently debating whether the fund can expand from buying and selling stocks, bonds and real estate into investing in infrastructure and private equity. Reforms of the fund are expected to be announced in April.
The governor of the central bank, Oeystein Olsen, told Reuters the deal was in line with the fund's mandate.
"The board (of the central bank)was specially informed about this deal because this was a special investment," Olsen said. "But also because it was a significant investment in an unlisted company."
The finance ministry, which sets the fund's mandate, declined to comment until it had first answered the queries by parliamentarians.
"The fund has to be able to defend its decisions politically as well as financially," said Steinar Juel, the chief economist at bank Nordea in January. "The fund could be undermined if it is perceived to make investments that are politically unacceptable."
The fund welcomed the interest from the parliamentarians.
"The oil fund is owned by the Norwegian people and we have received our mandate from the finance ministry," said Thomas Sevang, a spokesman for the fund.
"We think it is natural and good that the elected representatives of the people are interested in the the fun's management."