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Tuticorin-bound flights have also been diverted or cancelled.
Michaung is expected to subside into a deep depression over the next six hours, said an official.
The relentless downpour, reminiscent of the 2015 deluge, paralysed daily life, prompting authorities to declare a public holiday on Tuesday.
Many groups, that include children and elderly persons, are having a torrid time as they were forced to spend an additional 24 hours at the railway stations before they could manage to finally catch trains back home.
Actor Rahman had previously alerted about the dire conditions in Chennai, stating to Manorama Online that cyclone Michaung has inflicted substantial damage on the city.
The weather system is expected to persist till Thursday and thereafter become a deep depression and subside.
The cyclone is expected to make landfall on the coast of Andhra Pradesh Tuesday morning.
The southern railway has set up help desks for passengers at Chennai Central and Chennai Egmore.
The rains due to Cyclone Michaung, which is moving at the speed of 14 kmph in a north-northwest direction over the Southwest Bay of Bengal, have been battering Chennai for the past few hours.
Chennai and nearby Chengalpet, Kancheepuram and Tiruvallur districts among others received widespread rains since late Sunday.