The tweet was swiftly deleted and his office said the account had been very briefly compromised.
It is the second time Mr Modi's Twitter account has been hacked.
He's a prolific tweeter and has more than 70 million followers - the most of any world leader.
The deleted tweet from his main @narendramodi handle said the Indian government had officially bought 500 bitcoin and was "and distributing them to all residents of the country".
Last year, his account was hacked and a tweet sent out urging people to donate to a fake Covid relief fund.