City Public Prosecutor (CPP) M L Jegan filed the cases on behalf of Jayalalithaa before the Principal Sessions Court.
Swamy's comments in Twitter on September 20 allegedly ridiculed her, the CPP contended.
He submitted that Jayalalithaa was respected and supported in high esteem by the people of all sections and Swamy's statement was defamatory in nature and without any base and verification.
Another defamation case was also filed against Swamy in the court for his comments in the Twitter on September 17 regarding her assets.
A local court had on September 17 ordered issue of summons to Swamy to appear before it on October 30 in connection with a defamation suit filed against him over his remarks related to the issue of Tamil Nadu fishermen being detained by Sri Lanka.