Kiran allegedly made derogatory comments about Naidu, his son IT Minister N Lokesh and the state legislative council and also posted their caricatures and photoshoped pictures on Facebook.
Police said a decision on whether to arrest Kiran or not will be taken after questioning.
A member of the legislative council had complained to council chairman Chakrapani about the posts. The police were then alerted.
Ruling Telugu Desam Party (TDP) suspect the involvement of some YSR Congress leaders in what it calls a campaign on social media to defame its leaders.