One officer suffered head injuries, lost teeth and had to be taken to the Police Hospital, others had cuts to arms and legs and another had a broken hand, the daily El Pais (www.elpais.com.uy) quoted the Interior ministry as saying.
The match was held up for 11 minutes and police confiscated more than 100 firecrackers.
Penarol fans broke down barriers between the Amsterdam and Olimpica stands in an attempt to attack Nacional supporters. They also tore up seats and threw them towards rival fans.
When police stepped in to quell the fighting fans threw barriers at them.
The trouble began when Nacional supporters unfurled a banner they had stolen from Penarol fans in memory of Rodrigo Aguirre, a young fan shot dead in a clash of rival hooligans in 2011, according to Penarol vice-president Edgard Welker.
The "clasico", Uruguay's biggest match, has often been marred by violence off and on the pitch.
Penarol's young striker Jonathan Rodriguez contributed two goals to Sunday's victory.
Nacional would have gone top of the Apertura championship standings had they won. Instead they are in third place with 24 points from 12 matches, two points behind leaders Danubio.
Penarol, whose campaign has been mediocre, are eighth in the 16-team championship with 15 points.
(Reporting by Rex Gowar in Buenos Aires; Editing by Clare Fallon)
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