The violence came as the first 150 British combat troops of a deployment of about 3300 arrived in southern Afghanistan.
Habibullah Jan, a district government official, said Taliban or members of an allied faction were responsible for Wednesday's blast that hit the second of two police vehicles travelling on a road in Ghazni province, south of Kabul.
He said: "Militants who don't want peace and stability were behind this."
One of the wounded policemen was in serious condition.
The Taliban have been fighting US-led forces since they were ousted for harbouring Osama bin Laden weeks after the 11 September 2001, attacks on the US.
Violence has intensified in recent months with a wave of roadside and suicide bombings killing dozens of people as Nato members prepare to send thousands more peacekeepers.
Also on Wednesday, the bodies of two intelligence officers abducted while on a mission in Farah province in the west, were found in a desert on Tuesday, according to provincial governor Izatullah Wasifi.
He declined to speculate on who might have been responsible but Taliban have been known to operate in the province.
"Militants who don't want peace and stability were behind this"
District government official in Ghazni province
Earlier, police said security forces arrested a Taliban district commander in Ghazni province along with two of his men suspected of burning down a school.
Mullah Nazer Shah, the Taliban commander, had been a district official during the group's rule and was detained during a search by security forces late on Tuesday, Abdul Rahman Sarjang, the provincial police chief, said.
Shah's two men who were also detained were suspected of burning down a school in the area on Monday night in the latest attack on the US-backed government's efforts to promote education, he said.