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Arsenal identified on Tuesday that a number of their players had met Evangelos Marinakis, the Olympiakos owner, who has contracted Covid-19.
Marinakis visited the Emirates when Arsenal hosted Olympiakos in the Europa League on 27 February - 13 days ago - and came into close contact with club personnel.
Arsenal said that, according to medical advice, the risk of those who met Marinakis contracting coronavirus was "extremely low".
But government guidelines recommend that those who come into close contact with someone who has the virus must self-isolate at home for 14 days from the time of contact.
The players in question and four members of staff will now complete the one remaining day of their self-isolation period, making them unavailable to take part against City.
Arsenal, City and Premier League officials held discussions throughout Tuesday and duly announced the postponement of their Etihad meeting in the early hours of Wednesday morning.
In a statement, the Premier League said: "Following medical advice, Arsenal FC and Manchester City FC consider it is necessary to postpone their fixture due to be played this evening to give time to fully assess the situation.
"The Premier League has therefore agreed that tonight's game will be rearranged.
"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."
After the meeting between several players and Marinakis, Arsenal played third-tier Portsmouth in a FA Cup fifth round tie on 2 March and West Ham in a league fixture five days later.
However, the Premier League said that there are currently no plans to postpone further fixtures, with a full complement of games scheduled for this weekend.
On Tuesday, Spain's top-flight La Liga announced its next two rounds of fixtures would be played behind closed doors due to fears over the coronavirus outbreak.
France's Ligue 1 and Ligue 2 will not play with fans in attendance until 15 April, while five of nine matches in Germany's Bundesliga this weekend will be under similar restrictions.