Lamudin of Mannar in Sri Lanka and Mohammed Jasmin had come to India on labour visa and were staying with Indian nationals.
While Lamudin was staying with Indian national Nawaz Khan at a hotel in Ramanathapuram, Mohammed Jasmin was staying with Murugan.
Nawaz Khan has also been detained for questioning, police said.
The detention followed reports of security threat to some important shrines in the state including the Ramanathaswamy temple in this district, police added.
PTI