The Pentagon chief told an audience of civilian defense workers that he regretted the decision and had tried to limit the length of the furloughs while safeguarding the military's combat readiness.
"I'm sorry, but I have to be honest and deal with the facts. You deserve honesty and you deserve the facts," he said at a conference hall in Alexandria, Virginia.
An initial plan for furloughs of up to 22 days or 14 days had been scaled back after Congress approved additional funding.
But Hagel, describing a difficult set of choices, said he reluctantly concluded there was no way to avoid furloughs altogether.
"I could not go responsibly any deeper into cutting or jeopardizing our core missions on readiness, training. That is why I made a decision that we'll go forward with furloughs starting July 8 of 11 days," he said.
Nearly 69,000 civilians will be exempt from the furloughs, including intelligence officers, shipyard workers, those working in combat zones or in foreign military sales and some medical and police personnel, according to a memorandum issued by Hagel's office.
Under automatic budget cuts enacted by Congress, the Pentagon must slash its funding by roughly $37 billion through the end of the current fiscal year.
Asked by one employee if he could promise an end to further furloughs next fiscal year, Hagel said he could not offer any guarantees, as budget decisions were in the hands of Congress.
"What we're doing here is we're just trying to survive and get through this fiscal year," he said.
US commanders have warned the reductions will undermine military readiness by forcing cuts to training and maintenance.
Under mounting fiscal pressure, the Pentagon has already begun laying off temporary and contract employees and plans to scale back its civilian workforce by 5-6 percent over the next five years, according to Deputy Defense Secretary Ash Carter.
The Defense Department has proposed a budget for 2014 that would keep military spending steady at $526.6 billion, without taking into account the cost of the war in Afghanistan or the automatic budget cuts.
But the budget proposal may never be approved given the political stalemate in Congress, with both parties deadlocked over how to reduce the deficit.
The automatic budget reductions, or sequestration, were part of a 2011 law designed to contain the federal government's growing deficit and national debt.
Republican Senator John McCain mocked fellow lawmakers for allowing the budget cuts to go ahead for the military while taking action to avoid furloughs for civilian air traffic controllers.
"Our priority is air traffic control, by God, so we don't have to wait in line too long at an airport," he said.
"This is the most upside down, unbelievable, Alice in Wonderland experience when we're looking at the actual devastation of our ability to defend this nation."