Transport Secretary Grant Shapps said it is "completely unsustainable" that P&O Ferries chief executive Peter Hebblethwaite remains in position after nearly 800 seafarers were sacked without notice.
Mr Shapps told the Commons' Transport Select Committee "he will have to go".
The Cabinet minister also urged P&O Ferries to repay £11 million of furlough money, and said "they will have to pay the minimum wage" to crews.
His comments come as the firm's European Causeway ship remains in Larne Port after spending hours adrift off the coast of Co Antrim.
The operator said the ship had suffered a "mechanical failure."
Now, the Maritime and Coastguard Agency (MCA) has confirmed that, while the vessel has not been detained, it will have to pass another Port State Inspection before it sails again.
A MCA spokesperson said: “When any vessel reports an issue to the MCA, dependent on the nature of the issue, the MCA may undertake an inspection of that vessel.
"We generally follow up all issues reported on passenger vessels to ensure the safety of those onboard the vessel and that any issues are not so serious that they pose a threat to life or the environment.
"In the case of European Causeway we will be following up the incident with an inspection.”