The arrests were carried out in the province of Ankara, in addition to the southwestern provinces of Izmir and Aydin, the NTV broadcaster cited police as saying on Wednesday.
Karlov was shot and killed at an art gallery exhibition opening in Ankara on Monday. The Russian Foreign Ministry said it considered the attack a terrorist act.
Previous reports indicated that six relatives of the perpetrator have been detained. Some of them are reportedly linked to the so-called Fethullah Gulen Terrorist Organization (FETO), accused by Ankara of organizing a failed coup in July.