The announcement from Iran's military comes after media reports that staff at a bank in Tehran were killed in Israeli and U.S. airstrikes.
"The enemy has given us free rein to attack economic targets linked to the U.S. or Israel," it says.
Just hours after the warning, several companies in Dubai's financial district, including the major U.S. bank Citi and the British auditing and consulting firms Deloitte and PwC, closed their offices or urged their employees to evacuate as a "precautionary measure," sources told AFP.
The threat is likely to primarily affect Dubai in the United Arab Emirates - where many international financial institutions are based - as well as Saudi Arabia and Bahrain.
The military warning, issued via Iran's state media, says people in the region should not be within a one-kilometer radius of banks.
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