Prosecutors accused the pair of "making outrageous physical movements that did not respect the uniform, the morale and the value of national service".
The video, they added, was "an insult to the honour of military service".
The UAE is part of a coalition that has been battling the Houthi rebel movement in Yemen for almost nine months.
Its armed forces have suffered dozens of casualties there, and correspondents say this has made the authorities especially sensitive to the way they are portrayed.
The prosecutors complained that "some irresponsible persons were behaving improperly and in a manner that was certainly contemptuous of the local community which looked to its armed forces with deep respect and veneration".
