The A-League club released a statement on Tuesday night, in a cruel blow to the 28 year-old's immediate future - particularly after Wednesday's Socceroos' squad announcement for their upcoming 2018 FIFA World Cup qualifiers.
"The virus has caused inflammation in the area surrounding his heart and subsequently the player has discontinued training," City said in a statement.
"Franjic is currently under the care and assessment of a specialist cardiologist who has advised that he will make a full recovery."
Capped 20 times for the Socceroos, Franjic played 18 games for City during their 2015-2016 A-League campaign.
Franjic's condition comes after former Sydney FC starlet Chris Naumoff, 21, was forced into a premature, immediate retirement only last month, due to a genetic heart condition.
While Melbourne Victory captain Carl Valeri was also forced to miss the majority of last season due to an inflammatory condition affecting part of his brain.