Fenerbahce must also play their next home European match in an empty stadium and face a suspended one-season ban from UEFA competition after supporters threw fireworks from outside the stadium in the Europa League last 32 game with BATE Borisov.
That match was also played behind closed doors as part of an earlier punishment for Fenerbahce.
The Turkish club, thrown out of Europe last season for domestic match-fixing, have been fined 60,000 euros and the European competition ban is deferred for a probationary period of two years.
UEFA announced the measures in a statement on Wednesday which also included a ban for Fenerbahce's Raul Meireles in their last 16 two-legged tie with Viktoria Plzen next month after his red card against Borisov.
Rubin Kazan's Cesar Navas has meanwhile been banned for three European games after his last 32 dismissal against Atletico Madrid.
Lazio, who have a long-standing right-wing element among their fans, have paid the price for the continued racist conduct of their supporters.
Racist incidents have occurred in the home and away Europa League group matches with Tottenham Hotspur, the group match with Maribor and latterly Nazi salutes were witnessed in the last 32 home leg against Borussia Monchengladbach this month.
"The Control and Disciplinary Body decided to order Lazio to play their next two UEFA competition matches as host club behind closed doors. This applies to the following fixture: Lazio v VfB Stuttgart on 14 March," UEFA said.
"The remaining game behind closed doors applies to the next UEFA competition match for which the club would qualify. The Italian club have also been fined 40,000 euros."
LAZIO APPEAL
Lazio President Claudio Lotito, whose club had been warned after the Maribor incident that they faced a possible fan ban, was angry at the punishments despite the recurrent problems and said the Rome side would appeal.
"Two games behind closed doors, it's incredible," Lotito told Italian broadcaster Rai.
"We will appeal, that is certain. It's an abnormal sanction with respect to the reality, Lazio did everything we could and ought to have done to stop what happened.
"To suffer a punishment of one or two games behind closed doors, which will cause serious economic damage to the club and prevent fans from participating in an event like this, seems absurd to me."
UEFA were widely criticised for what pundits saw as lenient punishments handed out for racist behaviour by fans at Euro 2012. Denmark's Nicklas Bendtner was fined more for showing an advert on his underpants than federations were for racism.
Anti-racism campaigners have in contrast been enthused by the European governing body's actions on racism so far this year.
Serbia's Under-21 team had their spectator ban for racist abuse at last year's European Championship play-off with England doubled to two home games earlier this month after UEFA appealed its own disciplinary commission's verdict.
Italy's Serie A fined Inter Milan 50,000 eur
