The final two games of the ban are suspended and will come into effect only if Inter fans are the cause of further trouble during a probationary period of three years, European soccer's ruling body UEFA said on Friday.
In practice the ban means Inter will have to play without supporters for their next four UEFA competition home fixtures.
AC Milan were awarded the tie 5-0 on aggregate and will play PSV Eindhoven in the semi-finals.
AC Milan won the first leg of the quarter-final 2-0 and were leading Inter 1-0 when the game was stopped after 73 minutes when flares were thrown on to the San Siro pitch.
Inter are currently third in Serie A. If they finish in that position, or fourth place, they would enter the Champions League in the final qualifying round and play the home tie behind closed doors.
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The continued presence of Inter supporters at the Milan venue would then depend on their good behaviour and the 'suspended' two-match ban would be in addition to any separate sanction for a further offence, UEFA said in a statement.
The ban would also apply to the UEFA Cup and would be transferred to the following season if Inter were eliminated before playing four games.
Tuesday's match was the second time this season that a Champions League game in Italy had been abandoned due to crowd trouble. AS Roma's tie with Dynamo Kiev was halted after the referee was hit by an object thrown from the crowd.
UEFA ordered Roma to play two games behind closed doors.
As well as the fine, the ban will cost Inter heavily in terms of lost ticket revenue and other income.
Ticket revenue for Tuesday's game, which attracted a crowd of 82,000, was over 3.3 million euros ($4.25 million).
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