According to the Press Association UKAD took its decision because of a potential conflict of interest involving a member of its panel, and has therefore chosen to revisit the hearing at a date still to be confirmed.
The hearing, which began on Monday and was expected to conclude this week, was due to rule on allegations that Morecambe’s Fury and his cousin and fellow heavyweight Hughie Fury tested positively for nandrolone in 2015. It took until Wednesday for its postponement.
Both fighters deny using the banned anabolic steroid.
Those surrounding the Furys had been confident they would be exonerated, allowing Tyson - at 28 the older of the two cousins - to pursue the return of his boxing licence and a first fight since November 2015.
He has not fought since unexpectedly outpointing Wladimir Klitschko to win the WBA, WBO and IBF heavyweight titles, after first an ankle injury and then his struggles with depression prevented the scheduled rematch.
His improving condition had since led to him training alongside friend and fellow traveller Billy Joe Saunders, whose expected WBO middleweight title defence in London on July 8 against Georgia's Avtandil Khurtsidze he planned to fight on.
Fury instead again faces the prospect of waiting for the hearing to finally be concluded, then for UKAD's decision and any potential punishment he may receive, before attempting to recover his licence from the British Boxing Board of Control.
Frank Warren, who promotes both cousins, said: “We want to see the end of this. It's ridiculous.
"It's gone on and on. It's been over their heads for two years. It reflects badly on UKAD; it's taken all this time to get there and in the meantime there's no outcome. This is crazy.
"It's people's lives on hold, and it's wrong."