Investors in the Woodford Equity Income Fund should not be charged fees while trading in the fund is suspended, the chair of the Treasury Committee says.
Nicky Morgan also said the committee would raise the issue with regulators.
High-profile stockpicker Neil Woodford stopped money going in or out of his fund on Monday after increasing numbers of investors wanted their money back.
Bank of England governor Mark Carney has also warned about investments in assets that are difficult to redeem.
Treasury Committee chair Nicky Morgan said that investors in the Woodford Fund had been "locked out of accessing their cash" but that it had been reported that "Mr Woodford is taking in nearly £100,000 in management fees a day".
"The suspension of trading has provided Mr Woodford with some breathing room to fix his fund; he should afford his investors the same space and waive the fund's fees while the fund is suspended," Ms Morgan said.
She added that the Treasury Committee would "raise this troubling episode" when it spoke to City regulator the Financial Conduct Authority and the Bank of England.
Mr Woodford said this week that the suspension had been "necessary to protect investors' interests" after they redeemed about £560m from the fund over four weeks.
He said the fund needed time to reduce its exposure to illiquid and unquoted shares "to zero".
Illiquid stocks can't be easily sold quickly, and investors may make a loss on them, while unquoted shares are those in private, non-listed, companies.
In a speech on Thursday, Bank of England governor Mark Carney warned about investment fund exposure to illiquid assets.
The Bank of England's Mark Carney is busy rubbing shoulders with his counterparts from around the world in Tokyo.
But he's clearly aware of the growing frustration amongst the thousands of investors whose money remains locked in Neil Woodford's Equity Income Fund.
A spate of underperformance led investors to pull out half a billion pounds in the last month alone.
Now withdrawals are prevented while managers ensure there are readily available funds.
Some of the fund's assets were held in illiquid assets: shares in small companies that are hard to offload quickly for a profit.
Funds are allowed to hold up to 10% of their value this way, which can be lucrative.
In a speech, Mark Carney highlights that such practices are a growing trend that "promise liquidity…despite investing in potentially illiquid underlying assets" and so poses risks to the asset management sector around the globe.
The problem, as Mr Woodford has found, is that today's investors expect to able to get their cash quickly but still want a hefty return.
His fund's crisis isn't likely to be the last of its kind and may mean the rules come under intense scrutiny from regulators.