The protesters were prevented from marching on the presidency to complain about the population count in which they claim that blacks alone are required to produce documents to prove their nationality in the poor west African desert country.
These included papers that were often difficult to obtain such as the death certificates of great-grandparents, they claim.
Under the banner "Don't Touch My Nationality" (TPN), the group has been protesting for months, saying it fears that Negro-Mauritanians, mainly from the south, will be treated as second-class citizens or even expelled.
"One person is seriously wounded in hospital, a second is in the hands of the police and others are scattered through the city" of Nouakchott after Monday's protests, TPN spokesperson Birane Abdoul Wane claimed.
A police clampdown on a rally in September claimed the life of a demonstrator in Maghama in the south, followed days later by the arrest of 56 protesters in Nouakchott.
TPN demands the census be cancelled, deeming it "racist" and "discriminatory".
But the government of the largely Arabic-speaking nation has said it has no intention of stopping the count, which it says will help it establish "a modern and reliable" civil registry.
Political parties and rights groups gathered in Inal in the north of the country on Monday to commemorate the deaths of 28 black Mauritanian soldiers they claim were executed in 1990 as part of celebrations of independence day.