Estupinan did not return for the second half when Brighton lost 6-1 to Aston Villa over the weekend.
The 25-year-old has impressed with some energetic displays from the left side of defence for Brighton since joining from Villarreal last summer.
Estupinan has already scored one goal and assisted three times in six Premier League outings this season.
Last season, the Ecuadorian made 35 appearances in the top flight to help Brighton finish sixth and qualify for the Europa League.
"[Estupinan is] injured and can't play for a month," Brighton manager Roberto De Zerbi told reporters at a press conference on Wednesday.
"He's an important player we are losing, but we can play in that position with Tariq Lamptey, Igor Julio and other players.
"We have to be ready to change. We have to be good enough to get the result without important players."
"We are not used to playing so many games in a row in the same week and we have to adapt."
"To adapt we have to change many players game by game. The defeats against West Ham and Aston Villa are not because I changed a lot of players. I believe in my players and my squad. We have enough to fight better."
