The suspect is one of three people wounded in Tuesday evening’s attack, when men opened fire and threw explosives into a busy bar and restaurant in the coastal city.
“The suspect is one of those injured. He is now under police guard,” Iteere told a press conference in the Kenyan capital.
Iteere said the suspect had booked a bus ticket to leave Mombasa soon after the attack.
“We have retrieved a bus ticket from him and when our officers went to the bus station they found his luggage which had a magazine loaded with eight rounds of ammunition,” he said.
“We also got a laptop from him which we are analysing,” he added, noting that police had been watching the suspect for some time and were looking for him “in connection with various other attacks.”
In Tuesday’s attack one gunman opened fire when guards at the popular Bella Vista restaurant prevented him and two accomplices from entering, before the accomplices hurled two grenades and fled.
One of the grenades exploded near the entrance and the other near a car parked outside.
Since Kenya sent tanks and troops into Somalia late last year, it has been hit by a series of grenade attacks and explosions, mostly in Nairobi and in northern towns and camps housing Somali refugees close to the border.
Tuesday’s attack follows another set of twin attacks on the Mombasa region in late March in which one person was killed and 18 wounded.
Countrywide, targets have ranged from police vehicles to local bars to churches. The Kenyan authorities often blame such attacks on Somalia’s Al Qaeda-affiliated Shebab rebels.
Last month the Shebab warned Kenya of retribution and revenge attacks for joining the African Union force battling the insurgents.
The Kenyan Muslim Youth Centre, an organisation linked to the Shebab according to UN reports, hailed the attacks, saying that “grenades work very effectively” — although they did not specifically claim responsibility.
“This morning, who’s rejoicing and who’s mourning? Think about it. Leave Somalia!” one message on its Twitter site read. “One or two grenades in the right locations and boom goes Kenya’s economy.”
Earlier on Tuesday, a policeman was killed and two others seriously wounded when a landmine exploded beneath their vehicle as they escorted aid workers near the sprawling Dadaab refugee camp in northern Kenya.