The Games organising committee said there were too many doubts over the emblem for it to be used. A Belgian artist had complained that his design was stolen.
Logo designer Kenjiro Sano had admitted copying online material for a previous project, Japanese media reported.
In July, a new Olympic stadium design was scrapped amid a row over its cost.
The logo was unveiled only last month, based around the letter T and a red circle representing a beating heart - which critics said resembled the Japanese flag.
Its withdrawal is a highly unusual move.
Mr Debie expressed surprise at the organisers' decision on Tuesday as they had publicly backed the design only days earlier.
He told BBC Radio 5 live: "I thought the Olympic committee was a big machine and I didn't dare to take action against them."
But the director of the Theatre de Liege had told him they had to "do something" and they sought the help of good copyright lawyers.
He said the logo, devised in 2011, had been official for two years and would have been available on sites like Pinterest around the world.
While Kenjiro Sano has denied plagiarising the logo, he has admitted his team did copy other work for a beer promotion and faces several other accusations of plagiarism.
"I want Mr Sano to provide an explanation. I feel like we have been betrayed," said Tokyo Governor Yoichi Masuzoe.
-BBC