The report, by the Hurriyet newspaper, said on Tuesday that a Turkish security guard at the embassy was injured in the attack.
The wounded guard has been taken to a hospital for treatment. The report did not give further details.
Turkish police say they have already established the identity of the attacker, who remains at large, and whom the police are currently looking for.
A criminal case has been launched into the incident.
Qatari and Turkish officials have not made any comments on the incident, yet.
