The 'By The Way' rockers - also comprised of Flea, Chad Smith and Josh Klinghoffer - were due to perform at the Irish Capital's 3Arena on Tuesday (20.12.16) and Wednesday (21.12.16), but have put the shows on hold until the new year so that the 54-year-old rocker can get better.
In a statement, released via promoters MCD, the band said: ''We are so sorry that we cannot come to Dublin as planned for the next few days.
''Anthony has been fighting off the flu all week and after the show last night (18.12.16) it was clear that he has to stop touring and recover, hence the decision to push back the shows to next year.''
In May, the rock group had to pull out of their KROQ Weenie Roast headlining slot at the Irvine Meadows Amphitheatre in Irvine, California, and their planned performance for iHeartRadio after Anthony was rushed to hospital by ambulance with ''extreme stomach pains''.
The band's drummer Chad Smith revealed the medical emergency was ''really scary'', but said Anthony was ''on the mend''.
At the time, Chad said: ''His stomach was killing him (and) It was really scary. So we went directly to the hospital and we were really upset we couldn't play for the fans, but also more worried about him. I really appreciate all the well wishes. People sent so much stuff.''
American Thighs was released on this day in 1994.