The airport's Terminal 1 was shut down at around 11:30 am local time as police scoured the area for the 62-year-old man and was reopened after he had been apprehended.
About 2,500 passengers were delayed because of the incident.
Airport police said the man told them that as he rushed for his flight to Portugal he looked for the most direct route, accidentally going into the secure area through an exit, the DPA news agency reported.
A similar incident occurred at the same airport in March, when Terminal 2 was temporarily shut down after a 23-year-old woman went around security controls.
Police were able to find her and determined that she had simply been in a rush to catch her plane, but that incident meant delays for about 1,000 travellers.