The EasyJet flight had been due to take off at noon on Saturday, but was grounded when the woman said the Iraqi man next to her had messages relating to Islamic State on his mobile phone.
The suspicions have not been confirmed, Austria's APA news agency reported.
Security personnel initially removed the Iraqi man from the flight after which the whole aircraft was evacuated and routinely searched, while baggage was x-rayed again. The authorities were not able to find anything suspicious.
The flight finally took off three hours late, without the female passenger and the Iraqi man, who were questioned by detectives.
The mobile phone was also checked.
Links between the passenger, who said he was a student in London, and Islamic State had not yet been confirmed.
- DPA