The Point Pedro's Acting Magistrate issued their remand orders after they were presented before him earlier this morning.
The 19 fishermen were arrested last night and their two trawlers were also seized off the coast of Point Pedro in the north by the Sri Lankan Navy.
They were handed over to the officials of the Department of Fisheries and Aquatic Resources for further investigations, the navy said.
Fishermen violating each other's territorial waters has become a thorny issue in the Indo-Lanka relations and Sri Lankan parliament has debated the issue only yesterday.
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The lawmakers also suggesteed joint naval patrols to prevent fishermen from poaching in each others' waters.
The navy had on September 22 arrested 15 Indian fishermen for allegedly fishing in Lankan waters. In another incident on the same day, the navy personnel also chased a group of fishermen at gun point near Katchatheevu in Palk Staits besides damaging nets of more than 60 boats.