The suspects escaped Turkey in the days following the November attacks, the state-run Anatolian news agency reported on Sunday, quoting a statement from the Ankara security services.
Several of the detained are believed to have links with Azad Ekinci, who investigators suspect was a key planner of the bombings, the agency added. Ekinci is believed to have escaped Turkey.
Turkey has charged 21 people in the attacks that struck two Istanbul synagogues on 15 November and the offices of British-based bank HSBC and the British consulate five days later.
Turkish authorities at the weekend charged a man they said gave the final order for the attack on the Beth Israel synagogue.
Investigators said the suspect was apprehended with false identification trying to cross from Turkey into Iran.
Meanwhile, the bomber who detonated the truck bomb outside the offices of British-based banking giant HSBC has been formally identified by DNA testing, Anatolia said.
The man, whose remains were analysed at the Istanbul Forensic Medicine Institute and compared with the DNA of his relatives, was identified as Melvut Ugur, the agency reported.
The identification led to several arrests of the bomber's family members, it added.
Police have now identified four bombers who detonated explosives-packed trucks at two Istanbul synagogues on 15 November, leaving 27 people dead, and at the British consulate and HSBC building on 20 November, claiming 30 lives.