The fund was suspended 3 June due to the wave of redemptions from investors seeking to withdraw their cash, following a period of underperformance.
The suspension will run for a minimum of 28 days from Monday, but can be renewed.
Ms Morgan, who chairs the Treasury select committee, asked Andrew Bailey, chief executive of the regulator, whether fund houses that suspend redemptions should be allowed to continue to charge a management fee.
This comes after platform Hargreaves Lansdown called on Woodford to drop his fee after it itself dropped the platform fee for clients invested in the fund.
Woodford Investment Management insist the fee has remained unchanged during the period of the suspension, with the fund manager working every day to sell assets in order to raise enough cash to meet demands from investors who wish to redeem their holding.
Ms Morgan wrote: "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."
The MP for Loughborough asked five further questions she wishes Mr Bailey to answer ahead of his appearance before the committee on June 25.
These are what factors should dictate how long a suspension should be, and whether there was a maximum length; at what point the FCA would intervene in a suspension; whether the FCA had a view on the fees that funds charge during a suspension; and whether the FCA has initiated any formal investigation related to the events that led to the suspension.
Ms Morgan also asked for a timeline of the FCA’s supervisory contact with the fund or management; and a timeline of the FCA’s supervisory contact with the authorities in Guernsey, in relation to the fund.
The regulator has previously issued a statement reflecting on the fund's suspension in which it said it had been notified of the decision to suspend the fund but it does not approve suspensions.
It also said a suspension was "not an outcome the FCA seeks to avoid if it is in the best interest of fund investors" and that they are recognised as a legitimate tool internationally.
However, there was some controversy over the FCA's account of the fund's Guernsey listing.
The International Stock Exchange, which operates the market in Guernsey, contradicted claims made by the FCA when it said it had not been informed of Neil Woodford's decision to list some of his unquoted holdings on the island to ensure he met Uctis rules.
