Authorities seized the computer as the man passed through security at the airport at around 3:40 pm, a police spokesman said. The man then apparently fled inside Terminal 2.
Some 1,000 security officials started a massive manhunt at the airport. All passengers and airport employees were scrutinised before being allowed to leave the building.
Only hours later did police spokesman Albert Poerschke say the man, who has still not been identified, was most likely a businessman in a hurry to catch his flight who was unaware that security personnel wanted to check inside his laptop bag. He cautioned that the scanner could have been set off by chemicals such as perfumes.
"Although the facts were not too clear, the choice was made to take strong measures," Poerschke said. "We wanted to rule out anyone being put in danger."
The sealed off part of the terminal was for flights to the Schengen Area, where travellers are not required to show passports. The incident caused scores of flights to be delayed or cancelled.
Airports around the world have been on high alert since a Nigerian man was arrested and accused of trying to blow up an airliner over the United States on December 25 with explosive chemicals concealed on his person.