The Taliban did not immediately claim responsibility for the attack and could not be reached for comment, but the militant group carry out daily attacks on the country's army and police.
“The suicide bomber detonated his car near a residential area in Azra district of Logar, killing four army soldiers and seven local policemen,” Din Mohammad Darwish a spokesman for Logar's governor said.
Violence has increased in Afghanistan over the past year as foreign troops prepare to withdraw by the end of 2014.
The government is reluctant to release figures on casualties, but more than 4,000 police and soldiers were killed fighting Taliban insurgents in 2013 and this year's toll is expected to be higher.
Afghanistan's president Ashraf Ghani, who took office about a month ago after months of destabilizing deadlock over who won the election, said he hoped to achieve peace with the Taliban, Reuters reported.
"Peace is not easy but is a mandatory," Ashraf Ghani told a news conference in Kabul on Saturday, two hours after the attack. "If it was easy then it could be achieved during the past years."