The 66-year-old, who has a history of heart problems, will be treated with blood thinning medication for several months, said spokeswoman Lea Anne McBride.
"A major goal of treatment is to prevent further abnormal clotting in the body and to avoid complications such as the development of a blood clot in the lungs," said CBS News medical correspondent Dr. Jon LaPook. "The vast majority of these clots are successfully treated with blood thinners."
She said Cheney visited his doctor's office in Washington after feeling minor discomfort in his calf. An ultrasound showed the blood clot — called a deep venous thrombosis — in his left lower leg.
Blood clots that form deep in the legs can become killers if they break off and float into the lungs. This is called a pulmonary embolism.
There is evidence that such clots develop in people who take long airplane flights, reports CBS News White House correspondent Mark Knoller. The vice president returned last week from an overseas trip that included stops in Afghanistan and Pakistan, a trip that had him airborne for some 65 hours.
"When you're just sitting there with your legs hanging down for long periods of time, that's what predisposes you to the problem," said Sean O'Donnell, chief of vascular surgery of Washington Hospital Center.
"Treated properly, it poses a small threat," O'Donnell said. "Untreated and unrecognized, it's a very serious problem."
NBC correspondent David Bloom died in 2003 of a pulmonary embolism after spending days on end in a cramped military vehicle while covering the invasion of Iraq.
To fight DVT, airlines often encourage passengers to walk the aisles and wiggle their feet. But flying is not the only risk of DVT: it extends to anyone older than 60 or who has heart failure. Recent surgery, fractures, childbirth and taking birth control pills also can raise the risk.
Clots that form in the thigh are more likely to break off and migrate to the lungs than those that form elsewhere in the legs.
If the blood clot is caught early and treated properly, patients do very well, adds LaPook. Mortality is less than 5 percent.
Cheney, 66, returned to the White House after the medical exam and continued his work day.
"He'll maintain his regular schedule," McBride said. "He feels fine."
Cheney's health has long been an issue.
In 2005, he underwent six hours of surgery on his legs to repair a kind of aneurysm, a ballooning weak spot in an artery that can burst if left untreated.
He has had four heart attacks, quadruple bypass surgery, two artery-clearing angioplasties and an operation to implant a special pacemaker in his chest.
Doctors initially treat DVT patients with an anticoagulant medicine called heparin. Heparin was long given intravenously but can sometimes now be injected. That can eliminate or shorten a hospital stay. DVT patients are then given the blood-thinning drug warfarin, which sometimes must be taken for months.