The Californication rockers were due to play at the Irish capital's 3Arena on Tuesday (20Dec16) and Wednesday (21Dec16), but now will not play in the city until September next year (17).
The band apologised to fans in a statement posted on the Irish venue's website on Monday (19Dec16), writing that following a gig in London on Sunday (18Dec16), Kiedis needed time off the road to recover from the illness.
"We are so sorry that we cannot come to Dublin as planned for the next few days," the statement read. "Anthony has been fighting off the flu all week and after the show last night it was clear that he has to stop touring and recover, hence the decision to push back the shows to next year."
The shows will now take place on 20 and 21 September (17).