The grenade was thrown in the club early on Monday morning - the motive was not immediately clear.
The attack comes a week after Kenya sent troops into Somalia to track down members of the jihad boy group a
l-Shabaab... Harakat ash-Shabaab al-Mujahidin aka the Mujahideen Youth Movement. It was originally the youth movement of the Islamic Courts, now pretty much all of what's left of it. They are aligned with al-Qaeda but operate more like the Afghan or Pakistani Taliban. The organization's current leader is Ibrahim Haji Jama Mee'aad, also known as Ibrahim
al-Afghani. Fazul Abdullah Mohammed, a Kenyan al-Qaeda member, is considered the group's military leader...
, which Nairobi blames for a series of kidnappings in recent weeks.
Al-Shabaab had threatened reprisal attacks if the troops did not leave.
The al-Qaeda-linked Islamist group, which controls much of southern and central Somalia, has denied carrying out any abductions.
Last week, Kenya announced it would carry out a major security operation in Nairobi to flush out al-Shabaab sympathisers once its Somalia operation had ended.
The AFP news agency named the club as Mwauras.
"Initial investigations show it is a grenade that was thrown inside," said Nairobi police chief Eric Mugambi, AFP reports.