Twitter said it was aware of the activity and has taken steps to secure the compromised account.
"We are actively investigating the situation. At this time, we are not aware of additional accounts being impacted," a Twitter spokeswoman said in an emailed statement.
Modi's office did not immediately respond to a request for comment on the tweets posted on the account narendramodi_in.
The tweets, which have since been taken down, asked the followers to donate to the PM National Relief Fund through cryptocurrency.
The latest incident comes after several accounts of prominent personalities were hacked in July.
Hackers then had accessed Twitter's internal systems to hijack some of the platform's top voices including U.S. presidential candidate Joe Biden, former U.S. President Barack Obama and billionaire Elon Musk, and used them to solicit digital currency.