The India Meteorological Department (IMD) predicts the showers to continue throughout the day.
The worst affected was Ernakulam assembly constituency where voting at 12 noon touched a mere 20.80 per cent.
The other constituencies affected by rains are Vatiyoorkavu (voting 30.03 per cent), Aroor (35.65 per cent) and Konni (35.07 per cent).
At Ernakulam, CPI-M district secretary C. Mohanan said that he feels there is no need for deferring the polls on account of rain, as it has affected only a few polling stations and that people are coming out to vote.
State Congress president Mullapally Ramachandran said his party has full faith in the people who he hoped will come out and vote braving all odds.
"At Ernakulam there is a problem. The authorities should look into every aspect before making any decision," said Ramachandran.
State BJP president P.S. Sreedharan Pillai also sought to caution the authorities about objecively deciding the fate of the polls.
Historically, whenever there is a low turnout, the biggest beneficiary has always been the Left. The CPI-M, which has just one sitting MLA out of the five constituencies going to the polls, wants to wrest Vatiyoorkavu and, if possible, Konni besides retaining Aroor.
The BJP hopes to bag at least in one seat among Konni, Manjeswaram and Vatiyoorkavu, where in the last two seats, they stood second in the 2016 assembly polls.
"A few polling stations have been shifted from the ground floor to the first in Ernakulam Assembly constituency. Around 500 officials, including police, are making the arrangements. We will wait for the reports from the district collectors of the constituencies. We have made arrangements to transport voters to the polling stations in some places. If needed, we will extend the polling time as well," said Tika Ram Meena, Kerala's Chief Electoral Officer.
"In all these years, I have not lost the opportunity to cast my vote. I have never seen such rain on a voting day in my life, but I am determined to vote," said a 78-year-old nun, who arrived at a flooded polling station in Ernakulam.
In Konni, a constituency with a hilly terrain, voters living in higher areas are finding it hard to reach polling stations after flooding left several roads unmotorable.
A total of 9,57,509 voters, including 4,91,455 women, 4,66,047 men and seven transgenders, will decide the fate of 35 candidates at 846 polling stations in Vatiyoorkavu, Aroor, Konni, Ernakulam and Manjeswaram.
The polling began at 7 a.m. and will go on till 6.30 p.m. in the state.
( With inputs from IANS )