UEFA has charged United in relation to the fighting which broke out when Dynamo fans appeared to climb from the away section of Tannadice Park to get to the home support.
Home fans responded and fighting broke out, with police taking several minutes to get the situation under control.
European football's governing body has also charged United after supporters attempted to invade the pitch during the same game, which ended in a 2-2 draw.
A statement on United's website read: "Dundee United is carrying out an internal inquiry into the events during Thursday night's Europa League Tie v Dynamo Moscow.
"Any individual found to have been involved in unacceptable conduct and damaging the Club's proud reputation will face a stadium ban."
The case will be dealt with by UEFA's Control and Disciplinary Body on August 23.
The second leg of the tie will be held in Moscow this Thursday.
Source: AFP
Source: AFP