Several people were wounded in the attack, which took place in the Eastleigh suburb of the city.
Eastleigh is known as “Little Mogadishu” because of its large Somali population.
Eyewitnesses said devices appeared to have been thrown towards a bus stop and a food kiosk as people made their way home for the evening.
Kenya’s Standard newspaper said that the twin blasts went off some 50m (165ft) apart on 11th Street, and some of those caught up in the attack had serious injuries.
“We suspect it is a grenade,” a local police officer told AFP.
Eastleigh has seen several recent grenade attacks, including one in December last year that killed four people.
A week ago six people died when assailants burst into a church near the Kenyan port of Mombasa and opened fire on worshippers.
Kenya’s government has ordered all Somali refugees living in towns to move into designated camps in a bid to end the attacks.
Interior Minister Joseph Ole Lenku said the directive had been issued because of the “emergency security challenges” facing Kenya. A refugee group condemned the decision as illegal.
Kenya has several thousand troops in Somalia, helping the UN-backed government tackle al-Shabab, who are linked to al-Qaeda.
Although no group said it was behind the latest attack, many are blaming it on the Somali militant group al-Shabab.
Four members of the group were behind the four-day siege at a shopping centre in Nairobi last September, in which 67 people died.
The militants had stayed in Eastleigh before launching the attack.
President Uhuru Kenyatta has said Kenya’s tourism sector is “on its knees” because of the threat from Islamist militants.
Mr Kenyatta met ethnic Somali leaders last week to ask for their help in identifying people they thought may be behind recent attacks in the capital.
“We all have a responsibility to bring this to an end,” Mr Kenyatta said.