The expansion comes amid lockdowns across various parts of world on account of the coronavirus outbreak.
With schools and offices shut, people are turning to digital platforms for communicating with others as they practice social distancing to protect themselves against the pandemic.
Launched in 2017, Messenger Kids is a video chat and messaging app that helps kids connect with friends and family in a parent-controlled space.
"As many communities are managing response to COVID-19, with schools closed and people practicing physical distancing, parents are turning to technology more than ever to help their kids connect with friends and family, and looking to do so in a parent-controlled way," Facebook said in a statement.
Starting today (Thursday), parents in India will be able to download the app from the Apple App Store, and the app will be available in the Google Play Store by the end of the week, it added.
"For years, we've worked closely with Facebook's Youth Advisors, a team of experts in online safety, child development and media, to help shape the Messenger Kids app. We continue to consult child safety advocates and educators to ensure we're providing a service that balances parental control with features that help kids learn how to connect responsibly online," the statement said.
Every child account on Messenger Kids has to be set up by a parent. After downloading the Messenger Kids app, parents will have to authenticate the child's device using their own Facebook username and password.
However, this will not create a Facebook account for the child or give them access to the parent's Facebook account.
"Messenger Kids gives parents more control. Parents manage the contact list and have visibility into how their kids are using the app. Parents control kids' accounts and contacts through the Messenger Kids Parent Dashboard in their main Facebook iOS and Android app," the statement said.
It added that there are no ads in Messenger Kids and the child's information is not used for ads, and the app is designed to be compliant with the Children's Online Privacy and Protection Act (COPPA).