Fans found guilty of "unacceptable conduct" will be banned from Tannadice, the club have said. United travel to Moscow this week for the second leg, hoping to progress after the first match ended 2-2.
A statement on the club's website read: "Dundee United is carrying out an internal inquiry into the events during Thursday night's Europa League tie v Dynamo Moscow."
It added: "Any individual found to have been involved in unacceptable conduct and damaging the club's proud reputation will face a stadium ban.
"The club continue to foster the UEFA spirit incorporated within the RESPECT campaign and actively encouraged the promotion of these values in our strategy for Thursday's match and we are extremely disappointed that the actions of one or two individuals have been seen to damage what was yet another special European night at Tannadice."