A statement from the company on Sunday asked fans to "hold on to their tickets for now" amid ongoing efforts to save the Croke Park shows.
Refunds were due to start on Tuesday but that has now been put back to Thursday.
Ticketmaster said: "Ticketmaster understands that negotiations to try and find a resolution to the Garth Brooks concerts situation are still ongoing.
"As a result, Ticketmaster will be delaying commencement of the refunds process until 17 July. We would ask fans to continue to be patient and to hold onto their tickets for now."
American country singer Brooks had sold 400,000 tickets for the five concerts this month but Dublin City Council ruled that only three can go ahead.
During the week Garth Brooks rejected a compromise offer of two matinee shows and three night-time concerts saying it "cannot possibly compare" to the original five night run.