The bomber, dressed as a police officer, blew himself up at a police training facility in the country's Uruzgan Province on Monday morning killing 21 and injuring eight others, seven of whom are in critical condition.
The radical Taliban movement has claimed responsibility for the attack.
"The Afghan Interior Ministry condemns this terrorist act against those who protect the interests of its people," ministry spokesman Zemarai Bashary said.
Afghanistan's Defense Ministry also announced that three suspected terrorists had been arrested and were currently being questioned, a spokesman said.
"Details of the arrest will be given to the media after investigations have been carried out into the incident," the Defense Ministry's press secretary, Col. Zahir Murad, said.
Taliban militants have been behind hundreds of suicide attacks since they were forced from power in late 2001 by a US-led military coalition. The militants carried out more than 120 suicide bombings last year.
