Musk made the claims in an interview with the US Fox News host Tucker Carlson which will air later Monday.
The South African-born billionaire, who also leads Tesla and SpaceX, told Carlson that he was shocked to learn about the government's ability to read users' direct messages on his platform.
"The degree to which government agencies effectively had full access to everything that was going on on Twitter blew my mind," Musk said, adding, "I was not aware of that."
When Carlson asked if this included people's DMs, Musk replied, "Yes".
His comments caused an uproar on social media, with some users voicing shock and anger, while others seemed unsurprised given the US government's track record of surveillance and spying on its citizens at home, as well as allies and enemies abroad.
Musk bought Twitter last October for $44 billion after months of on-off negotiations. Since taking over as its CEO, he brought sweeping changes to the platform, from firing half of its staff, charging a fee for the verified accounts and reinstating the former US President Donald Trump on the platform.