A spokesman said the 33-year-old midfielder had been charged with the lesser offence of gross unsporting conduct which, according to UEFA's disciplinary code, carries a "suspension for one competition match or for a specified period."
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Gattuso will find out the extent of his punishment on Monday.
The charge of assault carries a minimum three-match ban and European football's governing body also has a provision for serious assault which would carry a minimum five-match suspension.
Gattuso has apologised for what he called "inexcusable" behaviour.
The former Italy international grabbed Jordan by the throat and pushed him out by the touchline during the Champions League last-16 first leg at the San Siro which Tottenham won 1-0 on Tuesday.
Gattuso also headbutted the Spurs assistant coach after the final whistle before being pulled away by team mates.
The Milan player has already been banned from the second leg after picking up a yellow card in Tuesday's match.
Former Scotland striker Jordan, with his trademark missing teeth during his playing days, won a reputation as a hard man in spells with Leeds United, Manchester United and AC Milan.
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