Delhi Home Minister Satyendar Jain said that voting started 50 minutes late at three polling booths.
"Voting started at 7.50 am at 3 booths of Railway Jhuggi, Shakurbasti," he tweeted.
However, there was no immediate response from the Chief Electoral Office.
Shashi Devi, a 58-year-old resident of Mayur Vihar I, said that she and her son were made to wait for 20 minutes by officials at a polling booth.
"My son and I came to cast our votes to avoid the heat, but after reaching the polling booth at 7 am, we were asked to wait for 20 minutes as officials were still in the process of starting polling," Devi said.
Another voter, Rahul Sharma, had to wait to for half an hour outside the polling booth of his area to cast his vote.
Among the early voters in the national capital were former chief minister Sheila Dikshit, Congress's New Delhi candidate Ajay Maken, Union minister Harsh Vardhan, BJP's East Delhi candidate Gautam Gambhir, and BJP national general secretary (organisation) Ram Lal.
Over 1.43 crore people in Delhi are eligible to vote in this election which will decide the fate of 164 candidates, of which 18 are women. There are 43 independent candidates.
While 2,54,723 voters are in the age group of 18 and 19, there are 40,532 electorate with disability who would be provided pick up and drop facility.