Tear gas was fired and one student died when he was run over by a police truck.
Earlier in the week, two people were shot dead during protests in a northern town after a court ruled that Mr Wade's third-term election bid was legal.
Elections in the West African country - often held up as one of Africa's model democracies - are due on 26 February.
'Fear of the unknown' Seydi Gassama, director of Amnesty International Senegal, told the BBC that Mamadou Diop, a 32-year-old student at Cheikh Anta Diop University, was run over - and a another female protester also died.
The opposition June 23 Movement (M23) had organised the demonstration and has sworn a campaign of "national resistance" until Mr Wade rescinds his candidacy.
Once a veteran opposition leader himself, Mr Wade, 85, was first elected in 2000 - ending 40 years of rule by the Socialist Party.
Senegal's constitution has a two-term limit but the constitutional court has ruled this does not include Mr Wade's first term, which began before the clause was adopted.
At the same time as allowing Mr Wade to stand, the court ruled singer Youssou N'Dour and two other opposition candidates could not run.
There has been international criticism of the ruling amid warnings that Senegal's long-standing record for democracy and political stability could be jeopardised.
Nigeria's former President Olusegun Obasanjo - himself a failed third-term bidder - told the BBC's Network Africa programme that "fear of the unknown" made leaders like Mr Wade hang onto power.
"But there is life after the government house - as I have found," Mr Obasanjo said.
Mr Wade's campaign spokesman, Amadou Sall, told the BBC if opposition supporters do not want Mr Wade as president they should go to the forthcoming polls.
"Every five years the Senegalese citizens have the right to express themselves… on 26 February if they decide they don't want no more Abdoulaye Wade for president, Abdoulaye Wade will not be president, so it's all in their hands," he said.