Kejriwal said the plan was to encourage women to use public transport, which is considered safest mode of transport.
"Metro is from certain point to another point - we have to take auto/bus in the night to reach home," a user pointed out, questioning the logic of free ride.
Former Congress spokesperson and current Shiv Sena leader Priyanka Chaturvedi took to Twitter to oppose the plan.
"With all due respect, women in Delhi didn't ask for a free pass to ride when they voted for Kejriwal ji, they had voted for the safe environment promised to them," she said.
"Hate to remind this, but Nirbhaya was gangraped in a bus in Delhi. At that time the country didn't protest over free rides for the women but for making the capital safe for its women to be able to take a bus or metro at any time of the day. Get your priorities right!," she added.
However, one user pointed out that the horrific incident occurred in a private bus.
"Typical Kejriwal law - women given free ride (irrespective of income level). But poor daily wage labourers will pay full fare. Nonsense," wrote another user, again questioning the rationale behind the plan.
However, the Delhi CM found support in filmmaker Pritish Nandy.
"Women in Delhi will get a free ride on buses and the metro. What a wonderful idea!," he wrote. "Will Mumbai emulate this? All the trouble we are going through for the construction of the metro will then be worth it," he said.
Kejriwal, in a tweet, thanked Nandy for his support. But many users criticised the filmmaker for his tweet.
"They should increase your tax rate to fund this. I think then it'll be fair :)," wrote one user.
"How many passengers are YOU willing to fund @PritishNandy? Start by putting money where ur mouth is, no?," wrote Anuraag Saxena.
Some, however, expressed hope that free ride for women in Metro and bus would increase the use of public transport by women.
"Very True. More women will take up public transport," said one female user.
( With inputs from IANS )