Morgan has been on trial with the Spireites but limped off after only 15 minutes of Saturday's 2-1 pre-season friendly defeat to Lincoln.
The 20-year-old was seen leaving Sincil Bank on crutches and it appears the former Liverpool trainee is set to go back to the Glovers.
"It's a bad knock," said Chesterfield boss Paul Cook. "Unfortunately for Adam it looks like he will go back to Yeovil now.
"It's a shame because he came in and he had opportunities within the squad. I'm disappointed for Adam because he needs to go and play football now.
"Unfortunately for Adam it doesn't look like it will be with us now, but we certainly wish him well."