* Attack comes week into Kenya's operation against Somalia rebels
* U.S. Embassy warned last week of "imminent threat" in Nairobi (Adds details, background)
By Yara Bayoumy and Njuwa Maina
NAIROBI, Oct 24 (Reuters) - A grenade attack on a bar in the centre of Nairobi early on Monday wounded 12 people, Kenyan police said, an incident that comes as Nairobi battles al Qaeda-linked militants in neighbouring Somalia.
Capital news radio quoted a witness who said a man had asked to be let in to the bar shortly after 3 a.m. (0000 GMT), when he hurled a grenade and fled the scene.
"It was a grenade attack. There are no deaths," central Nairobi police chief Eric Mugambi told Reuters, adding that of the 12, two had serious wounds in the leg and the face.
The blast came two days after the U.S. embassy in Kenya warned of an 'imminent threat' of a terrorist attack in Nairobi after the east African country launched a military campaign against Islamist al Shabaab rebels in southern Somalia.
Nairobi blames the militants for a wave of kidnappings of foreigners on Kenyan soil that have threatened the country's multi-million dollar tourism industry.
Al Shabaab had threatened major reprisals if Kenyan troops did not withdraw and the militants have launched large-scale suicide bombings in the past.
No one has claimed responsibility for the incident.
Reuters footage showed blood and beer bottles splattered on the ground of Mwaura's bar, which is frequented by blue-collar labourers attracted by its cheap beer and spirits.
Blood stained a sink and overturned seats and debris littered the floor. Police cordoned off the area as an officer examined damage on the walls from the force of the explosion.
"The guys came out running covered in blood. We helped them wash the blood off and they were carried away by ambulances," Jacob Musembi, a vendor at the scene, told Reuters.
"I'm very scared for my life because I don't know who they'll target next," he said.
A doctor at Kenyatta National Hospital said he had treated 13 people, some with serious wounds, but mostly with light head injuries.
Al Shabaab have denied responsibility for the Kenyan kidnappings, saying Nairobi was using them as a pretext for its military campaign.
Kenya has in the past initiated brief cross-border incursions, but the latest operation is on a much larger scale raising fears the country could be dragged into the anarchic Horn of Africa's two-decade-civil war.
The Islamist militants have proven capable of launching large-scale suicide attacks within Somalia and outside and have warned they would bring the "flames of war" into Kenya.
Earlier this month, a suicide truck bombing claimed by the militants killed more than 70 people when it exploded outside a compound housing government ministries in Somalia's capital Mogadishu.
The militants have also claimed responsibility for a bomb attack in the Ugandan capital, Kampala, which killed 79 people last year.
That strike, the militants' first on foreign soil, was in revenge for Uganda's contribution to the 9,000-strong AU peacekeeping force which is supporting Somalia's Western-backed government troops in ousting the rebels out of Mogadishu.
Nairobi is home to a large Somali community and last week security forces arrested two doctors for being members of al Shabaab. The militants also said three of their clerics had been arrested in Kenya, one of whom is on a U.N. sanctions list for recruiting new members and soliciting funds for the rebels.
Al Qaeda struck east Africa in 1998, killing hundreds of people, mostly Africans, in suicide bombing of U.S. embassies in Kenya and Tanzania. (Additional reporting by Noor Khamis; Writing by Yara Bayoumy; Editing by Matthew Jones)