The registration office is inside a Kandahar district government compound that includes administration offices, the police headquarters and a court.
The interior ministry blamed the attack on the "enemies of Afghanistan", a term often used by Afghan officials to refer to fighters linked to the Taliban, behind a wave of violence that also has roots in neighbouring Pakistan.
Three policemen were also killed on Monday in the eastern province of Paktia, bordering Pakistan, the interior ministry said.
The ministry added that five "enemies of peace and stability" were also killed when bombs they were planting into roads in Khost province, also on the Pakistan border, blew up prematurely.
The attack came as the Nato secretary-general said that internaional forces should not expect a quick withdrawal from Afghanistan.
"In my opinion, it is necessary to stay in Afghanistan for the foreseeable future," Jaap de Hoop Scheffer said.
"We will not be able to change Afghanistan into Switzerland in a few years time."
Barack Obama, the US president, on Friday announced a revamped US strategy to deal with the escalating violence.
The plan includes a greater focus on fighter sanctuaries across the border in Pakistan, an addition of 4,000 US military trainers to help the Afghan security forces and a ramping-up of civilian reconstruction efforts.
About 90 states and international organisations will meet in The Netherlands on Tuesday to discuss the situation in Afghanistan.