City said in a statement that the 60-year-old Italian had been struggling with the illness for more than a week and was referred to a respiratory specialist on the day of the game.
"The specialist felt the best course of action was for Guidolin to remain in hospital for a few days to receive further treatment," the club added.
Swansea said he was expected to recover fully in a few days and that his assistant Alan Curtis, who was interim manager until Guidolin's appointment in January, would deputise.
(Reporting by Toby Davis; Editing by Tony Jimenez)
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