The order, referred to as a "John Doe" summons was issued on 17 November, according to a report in The Guardian.
Experts told the newspaper that this was probably the beginning of a bid to try and pull digital currencies like bitcoin into the mainstream.
The IRS is seeking the details of all Coinbase users in 2013, 2014 and 2015.
Digital currencies are taxed in the same way that gold is, with capital gains tax to be paid when their value appreciates.
To back up its claims, the IRS cited three cases of anonymous users who had used digital currency to avoid paying taxes. Two of these were corporates with annual income of several million dollars; they used Coinbase wallets and hid bitcoin transactions as technology expenses on tax returns.
Some cryptocurrency experts told The Guardian that the IRS was making a test run after it had been blamed by the US treasury inspector-general for not doing enough to regulate digital currencies.
In a statement on 18 November, Coinbase said: "Our customers may be aware that the US government filed a civil petition yesterday in federal court seeking disclosure of all Coinbase US customers' records over a three-year period.
"The government has not alleged any wrongdoing on the part of Coinbase and its petition is predicated on sweeping statements that taxpayers may use virtual currency to evade taxes.
"Although Coinbase's general practice is to co-operate with properly targeted law enforcement inquiries, we are extremely concerned with the indiscriminate breadth of the government's request.
"Our customers’ privacy rights are important to us and our legal team is in the process of examining the government's petition. In its current form, we will oppose the government’s petition in court. We will continue to keep our customers informed on developments in this matter."