The Dubai government-backed port operator said the accident happened last week, on Thursday, but that there were no fatalities.
The company also says a second crane was shifted off its rails in the incident. An investigation is ongoing.
Security-camera footage of the accident obtained by shipping industry publication Splash 24/7 shows trucks moving on the dock moments before the yellow crane comes crashing down.
Jebel Ali is DP World's flagship port and the largest cargo terminal in the Middle East.
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