The Italian club were charged by UEFA in the wake of last week's Europa League game against Borussia Monchengladbach.
And, after incurring fines for similar incidents during the group stage games with Maribor and Tottenham, Lazio have been hit with a heavier punishment.
The ban on supporters will apply for the home leg of their last-16 tie with Stuttgart and the club's next game in European competition.
A fine of £35,000 has also been imposed for "the setting off and throwing of fireworks, racist behaviour and insufficient organisation."
Turkish club Fenerbahce, meanwhile, will host last-16 opponents Viktoria Plzen in an empty stadium after their fans launched a firework from outside the stadium during last week's game against BATE Borisov.
And UEFA has warned Fenerbahce - also fined £52,000 - will be banned from European competition for one season if there is a repeat offence within two years.
Both clubs have three days to appeal.