The whip was handed out at a sports arena in the city of Lashkar Gah, the spokesperson said.
According to the reports, each man received between 35 and 39 lashes and the audience included Taliban representatives, religious leaders, elders and local people.
The Taliban, who seized power in the country in August last year, have introduced hardline new rules that reflect their interpretation of Islamic law.
Last week, Taliban authorities announced the execution of an Afghan man for murder, the first public execution since taking power last August.