Balfour, an All-Star last season who notched 62 saves in 67 opportunities since he became a full-time closer in 2012 for the Oakland Athletics, had been lined up to replace closer Jim Johnson, who was traded to the Athletics two weeks ago.
"The Orioles are moving on from this situation," Orioles executive vice president of baseball operations Dan Duquette said on a conference call on Friday. "There was no contract. There was an understanding pending a physical exam.
"I guess the good news is we have other options to look at as we continue to try to improve our ballclub. But this is a situation where the deal's not going to come together.
"We would never say never or close the door, but we're going to turn our attention elsewhere for now, to look at some other options to try to staff our team and continue to build a contending team for 2014."
Duquette did not elaborate on what the deal-breaker was, but said the club's medical staff "wasn't satisfied" with the 35-year-old Balfour's physical exam this week.
However, Balfour's agent, Seth Levinson, released a statement later on Friday saying that the Australian was "completely healthy" and had been reviewed by two well-respected team physicians - Dr. Koco Eaton of the Tampa Bay Rays and Dr. Tim Kremchek of the Cincinnati Reds.
"Now factor into the equation that Grant was a 2013 All-Star, pitched 65 games and another three scoreless innings in the post season with a 94-95 mph fastball," Levinson's statement continued.
"The only reasonable conclusion is that Grant is healthy and the Orioles at the last moment changed their minds. Grant is an ALL STAR CLOSER who has converted 55 of his last 58 save opportunities."
Balfour, a Sydney native who will turn 36 later this month, was 1-3 with a 2.59 earned run average and 38 saves in 41 chances for AL West champions Oakland in 2013.
The right-hander, known for his tempestuous antics on the mound which came to be known as the 'Balfour Rage,' joined Oakland from Tampa Bay in 2011 after previous major league stops in Minnesota and Milwaukee in his 10-year career.