A number of supporters made their way on to the pitch in the closing stages of the encounter at St Jakob-Park, which European champions Real won 1-0 courtesy of a goal from Cristiano Ronaldo.
UEFA announced on Thursday that disciplinary proceedings had been opened in relation to the incident.
A brief statement from the organisation confirmed Basel had been charged with breaching regulations due to a "field invasion by supporters".
The statement added: "The case will be dealt with by the UEFA Control, Ethics and Disciplinary Body on 11 December 2014."
Basel are currently in pole position to join Real in qualifying from Group B.
The Swiss champions hold a two-point advantage over Liverpool, who they face at Anfield on December 9, and Ludogorets.
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