The 22-year-old frontman damaged his cruciate ligament in County's first pre-season friendly against Arnold Town in midweek.
"It's not good news. We're going to lose Jimmy for the whole of the season," Derry told the club website. "He's done his cruciate ligament.
"As it stands at the minute, it's not good. It's a major blow for us all."
After joining from Huddersfield Town in the winter transfer window earlier this year, Spencer scored five league goals in 13 appearances for County.