Police blamed "an error by a security officer".
Federal police spokesman Reza Ahmari: "An unauthorised person has come in an air security control in the security area and disappeared".
Travellers at Frankfurt Airport - Germany's largest - are now facing cancellations and long queues to re-enter the departure area.
The alert was resolved shortly after 2.30pm local time and the airport resumed operating as normal.
Police tweeted that the midday evacuation was prompted by a security assistant mistakenly allowing the French family of four into the secure area even though they were supposed to be subjected to a secondary screening.
The family were later located in the terminal, re-checked and allowed to continue on their journey.
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The police gave no details on what had triggered the original positive explosives test.
German police said they evacuated part of a terminal at Frankfurt Airport on Tuesday and stopped boarding due to "at least one unauthorized person in the security zone". More than 200 flights were cancelled and about 60 delayed.
Frankfurt Airport warned that disruptions to flights "can be expected" and advised passengers to check with their airlines.
A similar incident on 28 July at Munich Airport caused 300 flights to be cancelled, affecting 30,000 people.
It isn't immediately clear how many people were affected, but photos from the terminal show hundreds of people heading for the exits.