Manchester City were scheduled to host Arsenal on Wednesday, but the fixture will not take place based on medical advice.
In a statement, the Premier League said: "We understand this will cause inconvenience and cost to fans planning to attend the game but Arsenal, Manchester City and the Premier League have agreed that the short notice of Mr Marinakis' infection means there is no alternative but to take the time to complete a proper assessment of risk.
"All necessary measures are being taken and the Premier League currently has no plans to postpone any other matches."