The Minstermen, who require a point from their final fixture of the season after climbing out of the bottom two with victory over Southend at the weekend, have sold all of the 1,200 tickets available.
"The away allocation for Saturday's match at Dagenham is now sold out. Thank you for your wonderful support," it said on the club's official Twitter account.
York, two points ahead of second-bottom AFC Wimbledon with a vastly-superior goal difference, will be relegated straight back to the Blue Square Bet Premier Division if they lose and both Barnet and the Dons win.
But Nigel Worthington's side head to Dagenham on the back of a five-game unbeaten run.