The arrest came on the first day of fishermen resuming their work after the end of a 45-day-long annual fish breeding season ban on fishing using mechanised boats.
In a letter to PM Modi, Ms Jayalalithaa also flagged the issue of Sri Lanka reportedly trying to rebuild a church in Katchatheevu.
She said seven fishermen who had set out for fishing from Rameswaram yesterday were apprehended by the Lankan Navy early today.
She said it was their first day of fishing after the 45-day ban period and they were taken to Talaimannar.
Seeking to bring the resumption of fishermen's arrest to his "direct personal attention," she said, the "Sri Lankan Navy has escalated the frequency and magnitude of instances of abduction of our fishermen and the seizure of their boats and fishing equipment over the last two years."
She urged him to take up the matter with the highest authorities in Sri Lanka and secure the immediate release of the fishermen and a total of 89 fishing boats impounded on various occasions, without any delay.
The "Sri Lankan strategy," of not releasing boats and fishing gear of the state's fishermen, was causing great frustration among them, she said and requested him to direct the External Affairs Ministry to take immediate action in the matter.
Against the background of reports indicating efforts to rebuild a church in Katchatheevu, she said, "In a related provocative move, the Sri Lankan Government is trying to rebuild St Anthony's church on the disputed Katchatheevu Island without obtaining the consent and contribution of Tamil Nadu fishermen."
On May 14, she had said "the Indian fishermen from Tamil Nadu apprehend that if the church is demolished and reconstructed by the Sri Lankan side unilaterally, their traditional and customary access to this important place of worship could also be curtailed in the future."
She had urged the Centre to prevail on Colombo to involve Indian fishermen in the church rebuilding initiative.