Kenya's interior ministry tweeted a photograph of Malik Yassin and appealed for information that would help arrest him.
He is described as a tall and slim white man, with brown hair and brown eyes and speaking with a British accent.
"Malik Yassin, a British citizen, is suspected to have sneaked into the country and police have issued an alert for his arrest," the ministry said in on its Twitter feed.
"Police suspect that Malik is one of the al Shabaab foreign fighters of British origin," it added.
The interior ministry said another British jihadi, Thomas Evans, was killed in June during an attack on a Kenyan military base in the northern coastal region of Lamu County, near the Somali border.
Kenya has been on increased alert after various attacks by al Shabaab who are trying to get Kenyan troops and other members of an African Union force out of Somalia.
One of the worst attacks was in April when the Somali Islamist group in April stormed Garissa University, near the Somali border, and murdered at least 148 students.
The group was also responsible for the deaths of 67 people in 2013 when it attacked the Westgate shopping mall in Nairobi.
Kenya has in the past been a traditional transit route for Britons seeking to get to Somalia to join al Shabaab.
Convicted murderer Michael Adebolajo, who was responsible for the hacking to death in London of serving soldier Lee Rigby in 2013, was deported by Kenya after being arrested near the Somali border.
It is also believed that fugitive Samantha Lewthwaite, who was married to 7/7 bomber Jermaine Lindsay and is known as the White Widow, is believed to be hiding in Kenya.
She left Britain for East Africa in 2012 and is known to have links to al Shabaab.