The coastguard rescued five people and was searching for about 20 others who were still unaccounted for, the official told Reuters.
The coastline near the Tunisian port city of Sfax has become a major departure point for people fleeing conflict and poverty in Africa and the Middle East and searching for a better life in Europe.
"The boat sank about six miles from the coast of Sfax. Twenty bodies were recovered, five others were rescued, and all are from sub-Saharan Africa," the security official, Ali Ayari, said.
Around 45 people were on the boat when it sank, he added.