Morris will be allowed to return to his home in the Bahamas, as part of his bail conditions.
Morris is one of the principal holders of Bahamas-based Sierra Asset Management, a company that's alleged to have been a go-between for illegal transactions involving fixing the bid for the superhospital contract.
Executives with SNC-Lavalin – the company contracted by the MUHC to build the new superhospital – allegedly paid $22.5 million to Sierra Asset Management for a gas contract in Algeria that was never developed.
Police said they believe the money was instead paid to bureaucrats as a bribe to fix the superhospital contract bid.
According to the warrant, police believe Morris was the middle man in that process. The allegations have not been proven in court.
Police say former MUHC head Arthur Porter was one of the alleged beneficiaries of the transaction.
Porter has denied the allegations.
Morris was stopped by investigators on Monday at Montreal's Pierre Elliot Trudeau international airport on his way back from the Bahamas.
He faces charges of fraud, conspiracy to commit fraud, fraud toward the government and laundering proceeds of crime.