"The woman believed that she saw messages related to IS (Islamic State) on the man's mobile phone," Austrian interior ministry spokesman Karl-Heinz Grundboeck told AFP.
The woman alerted cabin crew, security staff were called, the takeoff was cancelled and all passengers and all their luggage were taken off the plane for checks.
"Nothing was found however, and the aircraft has since taken off, but without either the man or the woman. They are now being questioned," Grundboeck said.