Government officials in the northwest African nation had no immediate comment on the allegations brought by Amnesty International.
"Torture is used to extract confessions while detainees are being held in custody but also to humiliate and punish prisoners," said the report, prepared largely before Mauritania's August military coup.
Amnesty International said security forces carry out "routine and systematic torture of prisoners" with impunity to extract confessions.
"Torture is used against all categories of prisoners in Mauritania -- whether they are suspected Islamists, soldiers accused of involvement in a coup or those detained for simple ordinary crimes," said Gaetan Mootoo, Amnesty International's Mauritania researcher, who conducted the investigations.
The report cited statements from alleged torture victims who Amnesty International said gave "precise information about the people who tortured them."
"None of the acts have been investigated or their perpetrators brought to justice," the group said.
It also said Moroccan security officers sometimes participated in interrogations and torture, especially in investigations into acts of terrorism.
The vast Islamic country at the western edge of the Sahara has been a Western ally in the fight against terrorism.