Fans invaded the pitch at full-time after a heated confrontation between Bilel Mohsni and several home players.
The Scottish Professional Football League say the charges relate to "match organisation, security arrangements and supporter organisation".
A commission chaired by an independent senior solicitor will hear the case against the Premiership club.
Stressing that the charges "do not concern aspects of player behaviour which have been dealt with by the Scottish FA", a statement from the league body says the charges are for "alleged breaches of SPFL Rules in relation to alleged unacceptable conduct".
Motherwell won the match on 31 May 3-0 for a 6-1 aggregate success, preserving their top flight status.
Motherwell have been charged for the scenes that followed their play-off final win over Rangers in May.