The 21-year-old has impressed for the Whites since stepping up to the first team this season, scoring four goals in 12 Premier League appearances.
After netting his first senior goal as a substitute in a 3-2 defeat at home to Fulham in October, Summerville scored three goals in as many starts, including last-minute winners against Liverpool and Bournemouth.
Summerville was withdrawn on the 59-minute mark in Leeds' 2-2 draw against Cardiff City in the FA Cup third round last weekend following a strong challenge from Tom Sang.
The youngster is now set for a period on the sidelines and will miss Friday night's Premier League trip to Aston Villa.
Speaking at a press conference on Thursday, Marsch said: "Crysencio Summerville is out for a month, probably. The ankle injury and tackle he sustained in the Cardiff match is a little bit of a talking point for me.
"We're disappointed Cry will be out. He's hopeful that it will be quicker than a month but that's what the prognosis is right now."
Marsch added: "Between Cree and [Wilfried Gnonto] specifically, opponents have tried to bully them, they have a hard time containing them specifically when they're on the move in the dribble.
"Frankly, I don't believe the referees have protected those two players well enough, and it's put them susceptible to injury and hard tackles and I would like to see the referees protect attacking players more. So we're a little disappointed that Cree will be out."
On a positive note, Marsch has confirmed that Patrick Bamford has returned to training and will be in the squad for the trip to Villa Park, while Luis Sinisterra has stepped up his recovery from a foot problem, although Friday's game will come too soon for the winger.
Leeds currently sit 14th in the Premier League table, just two points above the relegation zone, and Marsch is expecting a "very difficult" test against Unai Emery's Aston Villa side on Friday.
"I would say in general I've seen a team that is more dynamic against the ball. They play a little bit differently with the ball as well. They're still very effective in set-piece situations and still what you know is that they have a lot of quality on the pitch," Marsch added.
"They have a lot of really good players and when they are confident, they are a very good team and very difficult to deal with.
"I know Unai Emery from playing against Villarreal with Salzburg in the Europa League. We lost 2-0 at home and 2-1 away. His team was very disciplined and defensively sound, but also dangerous in counter attacking situations, they had a lot of good players, and he has a lot of good players again.
"He's certainly a good manager and has made a positive impact on them, so it will be important for us to know going to Villa Park that we need to be at our best."
Meanwhile, Marsch has refused to comment on speculation linking Leeds with a move for Hoffenheim forward Georginio Rutter, who is allegedly set to undergo his medical before completing a club-record transfer to Elland Road.