The minister of electronics and information technology, Ravi Shankar Prasad, said the Central Bureau of Investigation will determine whether the British company violated Indian laws to manipulate the Indian electoral process.
Prasad said in Parliament that Cambridge Analytica has denied to the Indian government that data from Indians was breached, but that contradicted information received from Facebook.
The governing Bharatiya Janata Party and the opposition Congress party have accused each other of using Cambridge Analytica's services, but both have denied any link to it.
Prasad said a notice also was sent to Facebook in March, and it promised to improve its internal processes regarding hacking of personal data. "They also promised to take various other steps to ensure that such things don't recur," he said.
Cambridge Analytica declared bankruptcy this year following allegations that it used personal information harvested from 87 million Facebook accounts to help Donald Trump win the 2016 presidential election.
The Ministry of Electronics and Information Technology says Facebook's largest user base is in India.
Digital law experts say Indian regulations provide particularly weak safeguards against data breaches.