Somalia's interim government has ordered a night-time curfew in the capital, Mogadishu, as it struggles to end a wave of violence.
Somalia's police force are often targeted in attacks
At least five people were killed in the latest attack when a grenade was thrown at policemen in the main Bakara market.
Somalia's intelligence chief Mohamed Warsame Darwish said anyone on the streets between 1900 (1600 GMT) and 0500 (0200 GMT) would be arrested.
The attacks are blamed on Islamists and gunmen from clan militias.
"A masked man hurled a hand grenade at the police walking among hundreds of civilians shopping at the market," said chemist Ahmed Muqtar.
"I could see three people lying in the streets, one of them in a police uniform."
Another seven people were admitted to the Madina hospital, its director said.
Hawiye and Islamist fighters want Ethiopia to withdraw
The BBC's Mohammed Olad Hassan in Mogadishu says many stalls and shops closed, while police sealed off the entire area in the city centre.
"We need our forces to tackle the violence in the evenings and secure the city in order to prevent explosions. That is why we are imposing the curfew," said Gen Darwish.
Earlier this week at least two people were killed when insurgents attacked two police stations in overnight raids.
A government amnesty for Islamist fighters and leaders has failed to end the violence.
Ethiopian and government troops ousted the Union of Islamic Courts (UIC), the Islamist group that controlled most of Somalia for six months last year, in December.
Islamists and Mogadishu's dominant Hawiye clan are opposed to Ethiopia's presence in Somalia.
Tuesday's amnesty offer is seen as an attempt to persuade members of the UIC to attend next month's reconciliation conference.
The Islamists, however, insist that Ethiopian troops leave the country.
Some 1,600 Ugandan troops are in Mogadishu, the first contingent of a proposed 8,000-strong AU force, intended to replace the Ethiopians.
Somalia has been without a functioning government since 1991.