The bomb exploded about 10 miles north of Tirin Kot, the provincial capital of Uruzgan province, said Qayum Qayumi, the governor's spokesman.
In the capital, Kabul, a suicide bomber blew himself up outside a lawmaker's home, missing the parliamentarian but killing one person and wounding seven, officials said.
The bomber apparently thought lawmaker Bacha Khan Zadran was in a car pulling out of his compound, and the blast near the vehicle injured three people inside and five on the street, said district police chief Mohammad Khan Katawzi. One of the wounded on the street later died.
Katawzi said police in recent days had arrested a would-be suicide bomber who said his target was Zadran, a lawmaker from the eastern province of Paktia.
"The enemy of Afghanistan is clear, the terrorists who sabotage security, and they don't want me in Paktia," Zadran said. "They want to do more terrorist acts there."
The attack appeared to be the first suicide bombing in Kabul since mid-October. Taliban militants have set off more than 115 suicide bombs in Afghanistan this year in the country's bloodiest year of violence since the ouster of the regime in 2001.