The country's Interior Ministry singled out Mohamud, a senior leader of Al-Shabaab, on Twitter. He is also known by the aliases Dulyadin and Gamadhere, it said.
Mohamud is "credited with having an extensive terrorist network within Kenya," according to a Kenyan ministry document given to BraveheartNaija.
The ministry posted a "most wanted" notice for Mohamud. It offers a reward of 20 million Kenyan shillings, about $215,000.
"We appeal to anyone with any info on #Gamadhere to share with relevant authorities and security agencies," the Interior Ministry posted on Twitter.
Mohamud is in charge of external operations against Kenya, the document says, and he is the regional commander within Al-Shabaab in charge of the Juba region. In this role, he commands the militia along the border and "is responsible for cross-border incursions in the country."
His position as one of Al-Shabaab's top field commanders in southern Somalia has brought him into direct conflict with Kenyan troops deployed as part of African Union forces in the country.
"This is a man who has a lot of grudges against the Kenyans," said Stig Jarle Hansen, an associate professor at Oslo's Norwegian University of Life Sciences and author of "Al-Shabaab in Somalia: The History and Ideology of a Militant Islamist Group."