Spagnuolo said Avery will wait for the swelling in the knee to subside before having surgery.
"It looks like we'll lose him for the season, which is very unfortunate," Spagnuolo said. "He was having a terrific game. Donnie's a quality guy and a character guy and we'll miss him."
Avery, who led Rams wide receivers with 47 catches last year, was hurt during the second quarter of Thursday's preseason win over the New England Patriots. He jumped for Sam Bradford's long pass down the right sideline, fell and clutched his right knee as the ball dropped incomplete.
Before Avery was carted off the field, Patriots wide receiver Wes Welker went over and extended his hand. Welker is playing again after having surgery for a torn ligament in his left knee in February.
Avery, a second-round draft pick out of Houston in 2008, had 53 receptions as a rookie and started 28 games in his first two seasons. He caught 2 passes for 48 yards Thursday before being injured.
Information from The Associated Press contributed to this report.