Refunds may be delayed four to six weeks from mid-February, likely not showing up until late March, the IRS said.
The agency is working with tax-preparation businesses to deliver the refunds, said IRS spokeswoman Michelle Eldridge.
An H&R Block spokesman said the software problem had been fixed and the company was working with the IRS.
Two companies that provide online tax preparation software, Intuit Inc and Jackson Hewitt Tax Service Inc, said their programs were not affected and their education credit customers are not experiencing delays.
Various delays have hampered the tax season this year, slowing the arrival of refunds.
In February, some taxpayers who claimed earned income tax credits were hit by refund delays, the IRS said.
On Tuesday, a Wal-Mart Stores Inc executive said shoppers had cashed about $2.7 billion in tax refund checks at its U.S. stores so far this year. At this point last year, that amount was about $4 billion.
The IRS delayed the start of the tax filing season by eight days, to January 30, due to the enactment of tax law changes made to resolve the "fiscal cliff.
(Reporting by Patrick Temple-West; Editing by Kevin Drawbaugh and John Wallace)