The match between the two sides was abandoned. Sri Lanka lead the series 2-1 with one more ODI to go Jan 23 at Hobart.
Australia is also due to play Sri Lanka in the first of two T20Is at Stadium Australia, Sydney, Jan 26 with the second one at the Melbourne Cricket Ground Jan 28.
CA executive general manager Mike McKenna said they understood the fans' disappointment when the game was unable to be completed after a prolonged attempt to restore the playing arena after rain.
"Unfortunately, rain does affect cricket games from time to time but the circumstances with the large and - until that moment - very happy crowd last night were very unusual and we want to recognise that," he said.
The special offer is on sale for one day only and has been communicated by an email to fans who pre-purchased tickets before Sunday's game.
