United, who are due to play Kitchee FC in the stadium on Monday, have taken the decision after the torrential rain in the region over the last few days.
That match - the final game of United's five-match tour of Asia and Australia - would now appear to be at risk, with Moyes having admitted concerns about the pitch on Friday before further storms.
"Manchester United, Kitchee and the Hong Kong Football Association have reluctantly made the decision to cancel the open training session, planned for tomorrow (Sunday) evening at the Hong Kong stadium," read a statement on behalf of the club.
"The pitch has suffered from torrential rainfall in the last week, as well as staging a number of games in a very short space of time.
"Wednesday's matches (Sunderland vs Tottenham, Manchester City vs South China) had their kick-offs delayed, only proceeding after being shortened to 40-minute halves.
"The weather has continued to present problems for the pitch and the first consideration of both the HKFA and the club has to be the safety of the players in such conditions.
"The club has consulted with the Hong Kong FA and has also taken advice from Kitchee. In the absence of any other suitable facility, the open session has had to be cancelled."
Tottenham were able to complete their third-place play-off against South China on Saturday but heavy rain fell towards the end of the game, leaving visible sodden patches prior to Manchester City's meeting with Sunderland.
The saturated pitch has been under scrutiny since Wednesday when Spurs' Jan Vertonghen suffered ankle ligament damage after slipping on the surface, but Premier League chief executive Richard Scudamore denied that player safety had been compromised.