The band - famous for singing against Islamic extremism - was due to return on 11 October after performing at a peace concert in Amsterdam.
Kenya has not commented on their case.
Its government has been cracking down on Somali refugees and immigrants, accusing them of harbouring fighters from militant Islamist group al-Shabab.
'Children left behind'
The group is fighting to create an Islamic state in Somalia, and has also carried out a series of attacks in neighbouring Kenya.
The BBC Somali Service's Abdirahman Koronto says it is ironic that the band, Waayaha Cusub (The New Dawn), appears to have been targeted by Kenyan immigration authorities.
The band gained popularity for denouncing al-Shabab though its songs and one of its members, Shine Akhyar, was shot and wounded by suspected militants in Nairobi in 2007, he says.
Mrs Mohamud told the BBC Somali Service that she wanted to return to Kenya, where she had lived for more than a decade, because her three children were there.
However, she was scared of being deported to Somalia, she said.
"They [Kenyan immigration officials] told me if I return they will put me on a plane to Mogadishu," Mrs Mohamud added.
The Netherlands was now considering their request for asylum, she said.
Somalia has been hit by instability since the overthrow of long-serving ruler Siad Barre in 1991.
African Union and government forces have driven out al-Shabab from its urban strongholds, but the group still controls large swathes of territory in rural areas.