Financial details of the deal were not disclosed.
The Wall Street Journal, which first reported about the acquisition, said the transaction valued Kustomer at $1 billion.
Kustomer allows businesses to aggregate customer conversations from various channels into a single-screen, and also to automate some of the responses to buyers. The firm already offers its services on Facebook Messenger and Instagram.
Earlier this year, Facebook launched Shops, a service that allows businesses to display and sell products across its platforms.
(Reporting by Eva Mathews and Munsif Vengattil in Bengaluru; Editing by Shinjini Ganguli and Sriraj Kalluvila)