The hacking helped precipitate the diplomatic rift that has since opened up between Qatar and some of its powerful Arab neighbors.
Saudi Arabia, Egypt, Bahrain and the United Arab Emirates severed ties with Qatar in June over comments briefly posted on the Qatar News Agency attributed to its ruler in which he allegedly praised Iran.
Qatar said Sheikh Tamim bin Hamad al-Thani did not make the statements and that hackers had posted a false story on QNA, Reuters reported.
In comments published by QNA on Saturday, Qatar's Attorney General Ali Bin Fetais al-Marri said the suspects were being interrogated, without specifying their nationalities or any other details.
"Our friends in Turkey answered us a short time ago. Five people were detained and they are being investigated. Qatari prosecutors are working with Turkish authorities to follow this case," he was quoted as saying by Qatari media.
Marri has said Qatar has evidence that the hack was linked to countries that have severed ties with Doha for allegedly supporting militant groups and advancing the agenda of Iran in the region - charges Doha denies.
The dispute has defied mediation attempts by the United States and Kuwait.