The phosphorus bomb was discovered during construction work around the new Terminal 3, DW reported.
Airport operator Fraport had warned that flights may be disrupted as a result of the find.
Authorities cited by Germany's DPA news agency said a highway was closed and four runways could not be used while the operation to detonate the bomb was underway.
Fraport said on X, formerly Twitter, that any disruptions were expected to last until 9 p.m. local time (1900 UTC/GMT).
"Check flight status before traveling to the airport and allow extra time for your journey. We also recommend you check in as early as possible for your flight," the post on X said.
Later on Friday, police said the A5 highway had been reopened.
The discovery of unexploded World War II ordnance in German cities is not unusual.
The country experienced heavy bombing from Allied forces during the conflict, and explosive devices are frequently unearthed, especially at construction sites.
SD/PR