The game with Wigan has been put off because of a bad pitch.
Problems with the surface of the arena were highlighted after 65 games of rugby sevens during the Commonwealth Games, and now there are three affected matches.
The game with Bristol City was moved to Burton due to the cancellation of the Rotherham game.
There are ongoing issues with the surface.
Dave Boddy, the chief executive of the Sky Blues, said that moving more games wouldn't be possible.
He wanted the pitch to be safe and fit for purpose.
The situation is being monitored by the EFL, who are already discussing the implications regarding City's next scheduled home game.
An internationally established group of sports turf experts commissioned an independent report on the subject.
There is no maintenance work that can be done in time for Tuesday's game. The surface's current state would pose a risk to players and officials.
The league will now consider the circumstances of both postponements before determining what course of action could be taken and will remain in regular dialogue with the club over the work required to make the pitch safe.
Since the move of the rugby club to the city, the 32,000 capacity stadium has been owned by the team.
The contract to host Commonwealth Games events at the stadium was one of the reasons why the opening few home games of the season should have been switched.
They were aware of the schedule.
Even if we had been able to have our first three league games scheduled away, it is clear that the pitch would not have been usable.
There was no improvement in the pitch. This isn't the fault of the ground staff.
The quality of the pitch has not been fixed. In June, we were told that a new surface wouldn't be put in.
They met at the Arena on Monday, since they have been in contact via email.
The stadium was set up partly from a trust fund left by a Sky Blues fan after the controversial sale of their previous home for housing development.
After a dispute over rent, the Sky Blues spent 14 months in exile at Sixfields, Northampton.
After leaving their home at High Wycombe to buy the ground, the Wasps became City's landlords.
City played at St Andrew's for two seasons after a dispute with the other team.
The West Midlands Combined Authority gave millions of pounds of public money to the swass in June.
The rumour that the club is going into administration are not true, according to the owner of the club.
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