The chief of Somalia's Central Investigations Department, Colonel Abdullahi Hassan Barise, said the man was arrested at the Mogadishu airport on Tuesday and told authorities he was headed to Kismayo.
Kismayo is a southern Somali town under the control of the al-Shabab, the Islamist militant group aligned with al-Qaida.
Barise told VOA Somali Service the suspect said he had traveled from London to Nairobi and then to Mogadishu.
In an interview with VOA, government spokesman Omar "Yarisow" Osman said it is "very clear" the man arrived in the country to join al-Qaida in Somalia. "Very clear to us so far that this person was coming to the country to join al-Qaida in Somalia," he said.
Osman described the suspect as a 45-year-old British man.
Elsewhere, the Somali government said pro-government forces and Ethiopian troops seized control of two central towns in the al-Shabab-controlled Galgudud region. There are now only two remaining towns in the area still controlled by militants.
Al-Shabab has lost ground since last year, when Somali and African Union forces launched an offensive. Neighboring Kenya and Ethiopia have also sent troops into Somali to pursue al-Shabab.
In February, Britain hosted an international conference to discuss instability in Somalia and the regional threat posed by al-Shabab.
Britain's minister for international development, Andrew Mitchell, has said more British citizens are training alongside terrorists in Somalia than in any other country.