Starting linebackers DeMeco Ryans (groin) and Mychal Kendricks (calf) sat out practice for the third straight day as the Eagles prepared to take on an NFC East rival, the New York Giants, on Sunday night.
Also sitting out for the third day was running back and kick returner Chris Polk (hamstring) and Smith, a key contributor to the Eagles' special teams.
Ryans suffered his injury in the third quarter of last Sunday's win over the St. Louis Rams.
''It was a weird play,'' Ryans said. ''I made the tackle, and an offensive lineman just kind of rolled into me and hit me down low. I stayed in the game at first, but I saw I really wasn't helping the team so I came out.''
Ryans, who missed 10 games during the 2010 season with a torn Achilles when he was in Houston, has not missed a game since. He's played in 53 straight regular-season games plus three playoff games. The Eagles acquired him from the Texans in 2012.
Ryans said he's getting better. Asked if he could play Sunday without practicing this week, Ryans nodded.
''Could I?'' Ryans said. ''Yeah, I think I could handle it.''
Ryans leads the team in tackles with 49 total, including 35 solo tackles. He has one tackle for a loss and one fumble recovery this season.
Kendricks doesn't appear ready to go. He has been out since hurting his calf the second week of the season against the Indianapolis Colts.
Kendricks, one of the Eagles' top playmakers in 2013, was off to a good start this season. In the opener against Jacksonville he was credited with 13 tackles, a sack and three quarterback hurries.
With the Eagles on their bye next week, he's expected back when the team travels to Arizona, Oct. 26.
Smith, who plays special teams on both return and coverage units, had surgery earlier this week to repair what head coach Chip Kelly called a core injury. Smith had been listed on the Eagles injury report all week with a groin injury.
''He had a core injury and had surgery Tuesday to fix it,'' Kelly said. ''He'll be out a couple of weeks.''
Kelly said the injury was not a sports hernia, which would keep Smith out a minimum of six weeks, and maybe longer.
''No, the coach said. ''I think it's different.''
Rookie Josh Huff, who was active for the first time last week against St. Louis after battling a shoulder injury most of the preseason, will assume a lot of Smith's duties on special teams.
''(Smith) is a big contributor for us,'' Kelly said. ''But I think fortunately with Josh back and getting him a little bit more acclimated in there, his role will expand a little more from a special teams standpoint. He got his feet wet a little bit last week, but now we'll kind of pick up the slack in some of those areas.''
Huff, who had a kickoff return for a touchdown in the first preseason game, will also replace Polk on kickoff returns this week.