Cuba were set to play NC Dinos at the Dou Liou Baseball Stadium in Taiwan on Thursday as part of their preparations for the World Baseball Classic, which takes place from March 2-19.
"We have never experienced anything quite like this before," an NC Dinos official with the team in Taiwan told Reuters by telephone on Friday.
"It is customary for baseball teams from two different countries to have two different balls and to use balls of their choice (when fielding).
"But 40 minutes before the game, Cuba insisted both teams use the ball they chose," the official added. "We rejected that because our players could get injured by using balls they are not familiar with.
"We could not risk getting injured in a warm-up match like this one. Then they brought another ball, to which we again said no. They didn't give up and brought another one again and we turned them down once again.
"Finally, about 15-20 minutes before the game, they just abruptly notified us that they cancelled the game."
The official said Dinos had been taken aback by Cuba's decision to cancel the game.
"What they insisted was preposterous and goes against normal practice."
With no game to play, both sets of players started practising on the field.
"After the game was cancelled at the last minute, our team remained and practised in the stadium and the Cuban team didn't leave," the official added.
"So we practised there too for a while, the two teams in the same space, until we asked them to leave ... it was so awkward."
Dinos coach Kim Kyung-moon lamented the lost opportunity for his team to play one of the best international sides and said it would have been a valuable experience for his players.
Cuba are placed in Pool A of the WBC alongside champions Japan, Brazil and China.