The antitrust order also comes as WhatsApp sets out to expand its digital payment services to millions of Indians.
The Competition Commission of India (CCI) said WhatsApp had violated competition laws "through its exploitative and exclusionary conduct ... in the garb of policy update."
The 21-page order also asked its investigation unit to conduct the probe and submit a report within 60 days. Such probes typically take several months.
WhatsApp's conduct in sharing users' data with other Facebook firms, in a way that is "neither fully transparent nor based on voluntary and specific user consent", appears unfair to users, the watchdog added.
The CCI said WhatsApp had told the antitrust body that the policy update, which becomes effective in May, raised no competition law concerns.
WhatsApp did not immediately respond to a request for comment on Wednesday.
In India, users concerned about privacy have downloaded rival apps such as Signal and Telegram, according to data from research firms.