The plane entered Sardinian airspace before the crew was informed by an air traffic controller that the airport was closed to commercial traffic.
The Airbus A320, which was carrying only two passengers, landed back in Dusseldorf four hours and 10 minutes after its departure.
A Eurowings representative said the incident stemmed from a misunderstanding.
"Against the background of the corona crisis, the situation at numerous airports in Europe is very dynamic," the representative told CNN. "The large amount of information provided on operating hours or airport closures are often changed at short notice."
Olbia Airport was ordered reopened by the Italian Ministry of Infrastructure and Transportation on May 17, but the decision was overruled by a regional authority on the same day. The airport is currently scheduled to remain closed until June 2.
