Gareth Bale scored twice as Wales came from behind to beat their hosts 2-1 in their opening Euro 2016 qualifier, escaping a major upset to claim the three points.
A number of travelling supporters leapt over advertising hoardings to celebrate following Bale's winner nine minutes from time, but were quickly encouraged back into the stand by a combination of the Andorran stewards and Welsh players.
UEFA confirmed on Wednesday that they would be taking action over the incident.
The Andorran Football Federation are also facing charges relating to a lack of organisation at the Group B fixture, as well as for "improper conduct of the team", who received six yellow cards.
Sanctions over organisation at the match will come as an added blow to Andorra, who are already under fire for the quality of the artificial pitch at their new national stadium.
The cases will be dealt with by the UEFA Control, Ethics and Disciplinary Body on October 16.
