The game is controversial because many countries don't like how Zimbabwe is run by its harsh leader, President Robert Mugabe.
Should England pull out of the game, Zimbabwe will get all four points for winning the match.
That would make it extremely difficult for England to qualify for the second round of the competition.
The decision could also be very costly for the ECB.
They will have to pay a big fine to the tournament organisers for pulling out of the match.
Another effect could be that both Zimbabwe and South Africa refuse to come to England to play matches here this summer.
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Lizo Mzimba has the details
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