Weatherspoon, second on the team in tackles and sacks, injured the ankle in Sunday's 30-17 win at Philadelphia.
The loss of Weatherspoon, a first-round pick in 2010, is a significant blow to the NFL's only undefeated team. He played on every snap on defense this season before the injury.
"Spoon is a hard guy to replace," said safety William Moore, who also played with Weatherspoon in college at Missouri. "With Spoon being out this week, we're going to need for everybody to step up another notch. That's a big loss for our defense this week from a leadership standpoint."
Weatherspoon had 10 or more tackles in four games this season after setting career highs with 127 tackles and four sacks in 2011.
Smith provided no details on the severity of Weatherspoon's injury. Weatherspoon did not appear to be favoring the ankle when he walked through the locker room Thursday when reporters were conducting interviews. Weatherspoon declined an interview request.
Akeem Dent, a second-year player, will be the primary replacement for Weatherspoon.
"It's an opportunity for him to step up and play," Smith said of Dent. "We anticipate he will do a nice job."
Dent is the starting middle linebacker in the team's base 4-3 defense. But the Falcons play the majority of most games in their nickel defense with only two linebackers and a fifth defensive back, and that leaves Dent out of the equation.
The Falcons' nickel back, Robert McClain, played 90 percent of the defensive snaps against Philadelphia. Dent said he played only seven snaps in the base defense against the Eagles before replacing the injured Weatherspoon in the fourth quarter.
Dent filled in for outside linebacker Stephen Nicholas in the Falcons' 23-20 win over Oakland on Oct. 14 and had a career-high nine tackles.
"The good thing is he's going to be playing the same role he played when he filled in for Stephen," Smith said. "We kept him in his original role. He's very familiar with that role so it's not just training him in one week."
Dent's playing time is sometimes limited but he said he's always preparing for the chance to take a bigger role.
"Each week I go out in practice and continue to get reps within the nickel package," Dent said. "It's no different for me. I always watch Sean when he's in there and get mental reps if I'm not in the game or not on the field in practice."
Veteran outside linebacker Mike Peterson would join Dent and Nicholas as the three linebackers if the Falcons play their base defense.
Moore said Dent has played enough to show he can fill in for Weatherspoon.
"I think it's a gift and a curse for Spoon," Moore said. "You definitely don't want anybody going down, but it's going to show the leadership of Akeem and Mike Peterson to step up and raise their level of play."
Dent, a third-round draft pick out of Georgia in 2011, said he always practices as if he could play a bigger role.
"My thing is to always be prepared," Dent said. "You never know when there is going to be an injury in the game, like what happened last week. Something happened and snap, I'm the next guy in."
According to the Falcons' statistics, Moore leads the team with 63 total tackles. Weatherspoon has 60 tackles, four tackles for lost yardage, one forced fumble and one fumble recovery. His three sacks trail only John Abraham's team-leading seven.
Dent has 24 tackles.