An inquest into the death of Lance Corporal of Horse Matty Hull, 25, from Berks, was adjourned after the coroner said the tape was central to the case.
The MoD said it was classified "secret" by the US, so could not be released.
The Sun says the video shows US aircraft attacking a British convoy in Basra, southern Iraq, in March 2003. More on BBC
Shocking 15-minute video shows view from cockpit when US pilots hit British forces in Iraq. See Video here