The death toll by Amnesty is higher than the official number of 16 announced by the government.
The rights group says three children were among 23 killed. It said the deaths “including some by gunfire” were recorded in the capital Dakar and the southern town of Ziguinchor during the violent protests on 1 and 2 June.
“We call on the authorities to carry out a credible, independent and impartial investigation into the circumstances of these deaths and to ensure that those responsible for unlawful killings are prosecuted according to fair trial standards,” it said.
Senegal’s government had earlier said it had launched an inquiry into the protest deaths. It has not responded to Amnesty’s statement.
There has been a wave of recent protests in Senegal relating to the trial of opposition leader Ousmane Sonko.
Last week deadly protests erupted after Mr Sonko was sentenced in absentia to two years in jail for immoral behaviour, but cleared of rape charges.
His supporters say his charges are politically motivated.
