Schade, who dropped down to the bench for last weekend's defeat against Newcastle United, was named in the starting lineup for Saturday's clash with the Toffees at the Brentford Community Stadium.
However, the Germany international was unable to take his place in the side after suffering an injury during the pre-match warm-up.
The 21-year-old was taking part in shooting drills with his teammates when he fell to the ground holding his groin after striking the ball with his left foot.
Schade looked to be in serious discomfort as his teammates and members of the backroom staff approached him, before the medical staff arrived to assess the injury.
After being ruled out of the contest, Schade was replaced in the Brentford starting XI by midfielder Keane Lewis-Potter.
The Bees went on to experience a difficult outing, despite going into half time on level terms after Mathias Jensen had cancelled out Abdoulaye Doucoure's opener.
Everton retook the lead in the second through James Tarkowski, before Dominic Calvert-Lewin found the net just four minutes later to condemn Brentford to a second straight defeat.
The result leaves the Bees in 13th position in the Premier League table with six points to their name from as many matches.
Following the disappointing 3-1 loss, Brentford head coach Thomas Frank admitted that he was unsure about the extent of Schade's injury.
"To be fair, I don't know," Frank told reporters. "I guess it's not top, but I don't know the exact full picture of that. I was focused more on preparing Keane to be ready and it's not been at the top of my mind right now."
Schade's injury will come as a blow to Brentford, who recently received the news that Rico Henry is set to miss the remainder of the season after suffering an anterior cruciate ligament injury.
The Bees will now turn their attention to Wednesday's home meeting with Arsenal in the third round of the EFL Cup.