Sparano said he was unsure if Ferguson, who turns 35 on Saturday, will need surgery. He declined to elaborate on the specifics of the injury.
"We lost a heck of a player and another captain and those types of things," Sparano said. "It is happening every place you look around the league right now. That is what happens. It is Week 12. These guys understand and we have prepared for these things, so we will be prepared."
Ferguson has been in on 23 tackles in nine games for the Dolphins (5-5) this season. Dolphins running back Ronnie Brown (foot) and quarterback Chad Pennington (shoulder) have also suffered season-ending injuries this year.
"It's the nature of this game, though," left guard Justin Smiley said. "Sometimes you have to close ranks and march on. We're prepared to do that."
The Dolphins, who have propelled themselves back into the playoff mix with two straight wins and five in seven games, face the Bills (3-7) on Sunday, then meet the Patriots on Dec. 6.
"Those two are no cakewalk," Smiley said. "We've got Buffalo, who's hungry for a win, and those guys should have won the game last week. Obviously, everybody knows about the Patriots. ... We've got our work cut out for us."
"We had a situation where [Ferguson] wasn't in there before, had to play with some of these other guys in his place and they have done a good job," Sparano said. "I told the team that this morning. We have had some bumps, but the guys have responded really well. The guys who have gone in at different positions throughout the course of the season have done a great job."
Ferguson wasn't the only Dolphins player to leave Miami's 24-17 win over Carolina on Thursday banged up. Four offensive linemen left with injuries, and the Dolphins used three centers, including one moved from tackle who had not practiced snaps. When asked about one of the other injured players, Sparano said he would have updates later in the week.
"Nobody is going to feel sorry for you and if you start feeling sorry for yourself you are going to be on the wrong end of a real good butt-kicking," Sparano said of moving past the injuries. "We are not going to do that. We are going to get ourselves ready to go and go down there, try to win a division game, which is all our focus is about right now."