Ahmed al-Assadi, spokesman for the Hashed al-Shaabi umbrella group that includes mostly Tehran-backed Shiite militias, said the strike occurred on Saturday at 10:00 pm (1900 GMT).
“The initial report is that an Iraqi strike erroneously identified our forces as enemy forces and carried out a strike,” he told AFP.
“The drone struck with a first missile and then two more seven minutes later,” he said.
Assadi said nine members of the Ketaeb Jund al-Imam (The Battalions of the Imam’s Soldiers) militia group were killed and 14 wounded.
The Islamic State (IS) group was defeated in Tikrit and most parts of Salaheddin province last year but it maintains positions in the desert regions west of the Tigris.
“We were under attack, we called for ground support but when it arrived, the drone struck,” said Assadi.
He said the incident occurred near the sprawling Speicher military base, which lies northwest of Tikrit.
He said Prime Minister Haider al-Abadi had immediately opened an investigation into the incident.
The “war media cell”, which provides updates on the battle against IS on behalf of the Hashed as well as the interior and defence ministries, also said the premier’s office had launched an enquiry.
The US-led coalition which provides air support to ground forces battling IS said its aircraft were not active in the area at the time.