The 26-year-old defender rolled his ankle in the 1-1 draw against Burnley on Saturday and will not be involved at the King Power Stadium on Wednesday night.
Webster has been in superb form recently as Graham Potter’s side secured three straight clean sheets against Leeds, Tottenham and Premier League champions Liverpool.
Albion boss Potter is unsure whether the centre-half will recover in time for Brighton’s league game at home against Aston Villa at the weekend.
“Adam Webster isn’t too bad. He has a bit of swelling,” said Potter. “Wednesday is too soon and we’ll wait and see for Saturday.
“We’ll know more over the next few days but it isn’t a serious one, he’s rolled his ankle.”
Potter also confirmed that Solly March, who suffered a knee injury in the 1-0 win at Liverpool last week, is out for 12 weeks but has undergone successfully surgery.
“Solly has had his operation and it’s gone well, that’s good for him and us,” said the Brighton boss.
“The recovery will be slow but necessary, it’s a blow because he’s been really good, but that’s football.”
Tariq Lamptey (hamstring) , Alireza Jahanbakhsh (hamstring) and Davy Propper (groin) are all sidelined.
"The Leicester game will be too soon [for Propper],"said Potter. "He has an outside chance of Aston Villa, but more likely Crystal Palace.
"It has been a frustrating situation for Davy for different reasons but we will help him and support him through this last little set back.
"It is not a major one and we are expecting him back in the next few days and hopefully he can have a really good second half of the season as he's an important player for us."
Brighton have lost just once in 2021, a 1-0 defeat to in-form Manchester City, but Leicester present another tough opponent for Potter’s men.
“They are having a fantastic season, third in the Premier League and through in the Europa League as well,” said Potter.
“Brendan Rodgers is a top, top coach, they have very good players and have recruited very well. Their togetherness means that even when they might not have their first 11 out they are still a top team.”
Steven Alzate could be set for another midweek outing against the Foxes.
The midfielder scored the winner at Anfield last Wednesday but did not come off the bench in the subsequent draw at Burnley.
“Two days was a really short turnaround and he had a big night with 90 minutes at Liverpool,” said Potter.
“He hadn’t had that for a while so, just from a loading perspective, it was probably high risk going into the (Burnley) game.
“With the season he has had, with little bits of illness and injury, we just felt it was fair on him to see if he could help us off the bench.
“He wasn’t needed but it gives him chance to recover fully and we can think about him for the next match.”
Goalkeeper Jason Steele has recovered from a recent illness and is fit enough to take his place in the squad this Wednesday but Christian Walton, who played in the previous FA Cup round against Blackpool, is expected to start in goal.