The deputy provincial police chief, who is known only as Kamalludin, was at the scene when the bomb exploded but survived unharmed.
"I had just arrived with a five-vehicle police convoy. A man wearing police uniform walked towards us and exploded. Two of my bodyguards were also killed," he said.
Yousuf Ahmadi, a Taliban spokesman, said that a member of the movement had carried out the attack and claimed that 47 police officers had died.
Hamid Karzai, the Afghan president, condemned the attack, but said the fact that anti-government fighters were targeting police showed that they fighters were afraid of the force.
In a separate attack in Farah, a province in western Afghanistan, a would-be suicide bomber armed with a grenade killed a police officer guarding a compound , an Afghan official said.
The bomber was shot dead by other police as he tried to enter the compound and blow himself up, the official said.
The attacks come a day after a string of bombings killed at least seven people, including four Nato soldiers, in the south and east of Afghanistan.
There are about 70,000 foreign troops, including 38,000 US soldiers, stationed in Afghanistan. Washington is due to send 17,000 more troops to tackle the growing violence mainly in the south and east of the country.