A senior US legislator revealed the incident on Friday, which targeted the National Nuclear Safety Administration (NNSA).
It is the latest agency to reveal that sensitive private information about government workers was stolen.
The incident happened last September but energy department officials were not told about it until this week, prompting the chairman of the House of Representatives Energy and Commerce Committee to demand the resignation of the head of the NNSA.
An NNSA spokesman was not available for comment.
The NNSA is a semi-autonomous arm of the energy department. It guards some of the US military's nuclear secrets and responds to global nuclear and radiological emergencies.
Joe Barton, the committee chairman, said that Linton Brooks, the NNSA administrator, should be removed from office as soon as possible because he did not quickly notify senior energy department officials of the breach.
"And I mean like five o'clock this afternoon if it's possible," Barton, a Texas Republican, said in a statement.
Earlier this week, the Pentagon revealed that personal information on about 2.2 million active-duty National Guard and Reserve troops was stolen last month from a government employee's house.
That comes on top of the theft of data on 26.5 million US military veterans, the department of veterans affairs has said.
Sam Bodman, a spokesman for the energy secretary, declined to comment on the call for Brooks' resignation but said the secretary was "deeply disturbed about the way this was handled internally" and would make it a priority to tell workers about the lapse.
According to Barton, the NNSA chief knew about the incident soon after it happened in September but did not tell energy department officials, including Bodman, until Wednesday.