The amnesty was passed by parliament last October and entered force this month, the court said in a statement sent to AFP, adding that the "act of humanism" involves a total of 39,748 people.
It said the amnesty focused on women, minors, men over 60 and foreign nationals and was timed to coincide with 24 years since the passing of the country's Constitution.
Uzbekistan has held regular amnesties since soon after its late leader Islam Karimov came to power in 1991.
Karimov died in September at the age of 78 after suffering a stroke. He had held onto power since winning Uzbekistan's first elections after the fall of the Soviet Union.
More From This Section
His authoritarian rule came under fire over accusations of heinous rights abuses.
Interim leader Shavkat Mirziyoyev won a crushing presidential election victory in an uncompetitive vote in December.
Amnesty International in a report released last April said that there was "overwhelming evidence that torture continues unabated in Uzbekistan".