The Somali al Shabaab Islamist group has claimed several attacks on Kenya in the past.
After a raid by gunman at a Nairobi shopping mall that killed at least 67 people in September, the group said it planned more attacks. The coast, which is popular with tourists, has been a target.
Al Shabaab have demanded Kenyan troops withdraw from Somalia, where they have been fighting the Islamist rebels.
Mombasa police chief Robert Kitur said: "Our first suspicion is that they are al Shabaab especially because of their origin."
He said one man was Somali and the other was a Kenyan of Somali origin.
Police tracked the men and recovered two large improvised explosive devices from them.
Mr Kitur added: "We suspect they were planning to detonate them somewhere around Mombasa. If they had detonated, they would have caused massive destruction."