Amol Jadhav, a city resident, had filed a complaint against Mr Gandhi and Twitter.
President of the commission Pravin Ghuge said he has sought a reply from both as to why action should not be taken against them under the Juvenile Justice Act, 2015 and the Protection of Children from Sexual Offences Act, 2012. As per the law, identity of minor victims can not be disclosed.
The commission has sought a reply within 10 days.
"I issued notices to (Rahul) Gandhi and Twitter as they have disclosed the identity of victims," Mr Ghuge told news agency PTI.
Mr Gandhi had tweeted about the incident tagging the video, and blamed the BJP and RSS for rising atrocities against backward classes.
Mumbai Congress chief Sanjay Nirupam dismissed the notice, calling it nonsensical.
"The notice is nothing but bakwaas (nonsense). The notice should have been sent to the Maharashtra chief minister who has failed to protect the rights and dignity of children. Rahul Gandhi simply highlighted this sorry state of affairs," he said.
Follow NDTV for latest election news and live coverage of assembly elections 2019 in Maharashtra and Haryana.
Subscribe to our YouTube channel, like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.