Weatherspoon suffered the injury while running under the supervision of the team's medical staff.
Weatherspoon had been held out of the organized team activities as he was continuing his recovery from a foot injury that limited him to only seven games in 2013.
The loss of Weatherspoon, the team's first-round pick from Missouri in 2010, is a blow to the Falcons, whose disappointing 4-12 finish in 2013 was marked by a string of injuries. Weatherspoon has eight sacks and two interceptions in his first four seasons.
Weatherspoon has managed to play a full 16 games in only one season, 2011, when he had 80 tackles and a career-high four sacks.
Coach Mike Smith said in a statement released by the team on Tuesday night Weatherspoon is expected to make a full recovery following surgery.
''During Sean's run today with our medical staff, he suffered an injury,'' Smith said. ''We sent Sean to the doctor for some additional testing and evaluation and unfortunately the results showed that he ruptured his Achilles tendon.
''Sean had been working extremely hard to get back on the field, but regrettably he will miss the entire 2014 season. He will have a procedure done in the near future and we expect him to make a full recovery.''
Before Weatherspoon's latest injury was disclosed, Smith said Tuesday that Bartu and Worrilow have matured in the offseason.
''Two guys who ended up playing a bunch of snaps for us last year have improved and matured,'' Smith said, referring to Worrilow and Bartu.
''If you would have told me at this time last year that one was going to be our leading tackler and the other was going to play 70 percent of the snaps I would have said 'I don't think so.'
''They are a much more mature group. We went through some growing pains with them last year that are going to pay dividends moving forward.''
The Falcons added four linebackers late in this year's NFL draft.
Notre Dame's Prince Shembo was selected late in the fourth round. Syracuse's Marquis Spruill was the team's fifth-round pick. Connecticut's Yawin Smallwood and South Dakota's Tyler Starr were seventh-round picks.
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