Kenyan police have arrested more than 650 suspects in a crackdown on suspected Islamist insurgents following a bomb attack which killed six people in the capital Nairobi.

"This act of cowardice perpetrated against innocent and peace-loving Kenyans who were going about their normal activities is barbaric," Interior Minister Joseph Ole Lenku said in a statement.

"So far 657 suspects have been apprehended," he added.

Kenyan police regularly arrest scores of people after similar attacks in sweeping security operations, but later release most after questioning.

The three blasts on Monday evening targeted two small restaurants and a local clinic in a particularly densely populated area of Eastleigh, an area often known as Little Mogadishu because of its predominantly Somali population.

No one has claimed responsibility for the blasts, but Eastleigh has in recent years been the scene of several explosions, usually attributed by the police to Islamist extremists.

The attack comes a week after six people died when assailants burst into a church near the port city of Mombasa and opened fire on worshippers.

Kenyan authorities last month ordered all refugees, most of them Somalis, to report to two overcrowded camps, a move criticised by rights groups and the United Nations.

However, police argue the move is necessary for security.

Kenya has been hit by a series of attacks since sending troops into southern Somalia in October 2011 to battle Al-Qaeda-linked Shebab insurgents.

The Islamists claimed responsibility for the most deadly attack, in which they laid siege to Nairobi's upmarket Westgate shopping mall in September, killing at least 67.

The Shebab have warned Kenya of renewed attacks, with Kenyan troops taking part in a renewed African Union military advance on bases of the insurgents in Somalia.