The 36-year-old failed to recover from a torn calf muscle, an injury which has now put him in doubt for England's Ashes opener in Edgbaston in just over a week's time.
Anderson sustained a minor tear to his right calf muscle while playing for Lancashire against Durham in Sedburgh on July 2.
He has not bowled competitively for almost three weeks, and did not bowl during England's training session on Monday after feeling some discomfort.
England had been optimistic about his recovery with national selector Ed Smith intimating that Anderson may play with a limited workload against Ireland.
However, when he could not bowl during the training session, the team management decided to take no risk with the veteran seamer.