They also seized six mechanised boats, M Gopinath, Rameswaram Fisheries Assistant Director said.
The fishermen and the boats have been taken to Talaimannar.
They were part of a group of fishermen, who set out in 727 boats from here last night and while they were fishing near Katchatheevu, the Lankan Navy personnel came in four boats and arrested the 29 fishermen.
They allegedly damaged the fishing nets of about 20 boats and threw them into the sea, he said.
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Talks between India and Sri Lanka on the fishermen issue had ended in deadlock early last month and negotiators are scheduled to meet again this month.
Sri Lanka had shot down a request from Tamil Nadu fishermen to allow fishing in Lankan waters for 70 days a year and to allow bottom trawling.
Katchatheevu, an islet in the Palk Straits, was ceded to Sri Lanka by India in 1974.