The bomber detonated a vest full of explosives in a police compound used for training exercises in Tirin Kot, the capital of Uruzgan province, Uruzgan police chief Juma Gul Hemat told Reuters.
The Interior Ministry confirmed the attack.
"As a result of the suicide attack on a police unit ... 21 police were martyred and eight more wounded," the ministry said in a statement, according to Reuters.
Taliban insurgents claimed responsibility for the attack, according to Reuters.
The bombing marked the second suicide attack in as many days in Afghanistan. On Sunday, on the outskirts of Kabul, a suicide car bomber rammed a vehicle filled with explosives into a military convoy. Three people were injured, including a French soldier.
Two weeks ago a suicide bomber struck near the German Embassy in Kabul, killing four civilians and an American soldier.
U.N. special representative to Afghanistan Kai Eide said the attack showed "contempt both for human life and for the community's wishes for a just Afghanistan," the BBC reported.
In 2007 about 140 suicide bombers struck Afghanistan, according to the New York Times. As security has tightened, the Taliban has turned to more roadside bombs, in 2008 there were only 80 suicide bombings but the number of roadside bombings doubled.
The U.S. has spent about $6.2 billion training and equipping Afghan police since the U.S. mission in Afghanistan began seven years ago, according to the Washington Post. Over the past several years, Afghan police have increasingly borne the brunt of these attacks.
More than 900 Afghan police were killed in 2007 and 868 were killed in 2008, according to the Associated Press.
U.S. military officials have requested an additional 2,300 trainers to help expand the Afghan police force from 62,000 to 82,000 over the next couple of years.
Last week, Afghan officials said that the country's second-ever presidential election will be postponed three months until Aug. 20 to give them more time to prepare. The delay also would allow more time for the additional U.S. troops to arrive.