Thousands of hectares of farmland including those ravaged by last year's tsunami were flooded by the rains, but there were no reports of casualties, the officials said.
A landslide triggered by the heavy rains cut off a road in the Kodaikanal hill station and stranded some 10,000 people living in seven villages.
"More rains are expected over Tamil Nadu and adjoining Pondicherry in the next two days due to the presence of the feeble trough of low pressure over the southwest Bay of Bengal," a meteorological department official said.
On Saturday, Tamil Nadu's 55 million people breathed a sigh of relief after Cyclone Fanoos weakened just before landfall, but heavy rains in the Rameswaram district forced authorities to suspend train services.
Last week, 21 people died and 175,000 people were forced from their homes after cyclone-induced heavy rains sparked floods in four Tamil Nadu districts including the state capital Chennai.