The announcement comes after media reports that staff at a bank in Tehran were killed in Israeli and US airstrikes.
"The enemy has given us free rein to attack economic targets linked to the US or Israel," it says.
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.
People in the region should not be within a one-kilometer radius of banks, reads the military warning, which has been issued via Iran's state media.
