The man had boarded a flight to Lubumbashi in the Democratic Republic of Congo at the Jomo Kenyatta International Airport (JKIA).
The man, who police circulated his photograph, was holding a German passport.
He was then handed over to the anti-terror police for questioning.
It was not immediately clear how long he had been in the country. His flight was to depart JKIA at 7.35am.
Detectives told Nation that the man resembled Mr Erdogan, who they suspect was behind the blast that has so far claimed one life with 35 others injured. Police had indicated that it was not clear whether the suspect was a Turkish or a German national.
It is suspected that he might have entered the country on May 3 together with another Swiss national Magd Najjar and proceeded to Eastleigh in Nairobi.
At JKIA, the man told detectives that he was destined for Lubumbashi.
The man insisted that he was a manager of a power project in Kinshasha but opted to go through Kenya since he could not go by road owing to the war in the region.
“He told us that he had gone to Germany to purchase some electrical equipment,” said one of the detectives who was interrogating the man.
On Thursday, one of the four people who were admitted to the Kenyatta National Hospital following the blast succumbed to her injuries.
Hospital spokesman Kibet Mengich said the patient, who was admitted to the Intensive Care Unit (ICU) after suffering 90 per cent degree burns, died at 6.45am Thursday.
Following the death, one patient with 50 per cent degree burns is still admitted to the ICU while two others suffering from spinal shock and post-stress disorder are admitted in wards 6D and 8D respectively.
When releasing Mr Erdogan photo on Wednesday, police spokesman Eric Kiraithe appealed to the public to volunteer information.
“Any person with information on this person should provide the same to the nearest police station. He is believed to be either a citizen of Germany or Turkey and traveling on fake or forged papers,” he said.
Mr Kiraithe said police had established that the lunch-hour explosion was caused by an improvised explosive device “planted in the building by criminal elements”.