Frimpong ruled out for up to nine months
The 18-year-old had been expected to break into the Gunners' first team this season and manager Arsene Wenger described Frimpong's setback as a "massive blow."
The Ghanaian-born Frimpong's injury comes after news that French midfielder Samir Nasri will be out for about four weeks after undergoing surgery on a knee problem.
"Samir's injury is a blow for us and a blow for France as well," Wenger said on Arsenal's website on Thursday.
"But we have had another blow with Emmanuel Frimpong. He has done his cruciate in training. That is a massive blow. A cartilage is three to four weeks but a cruciate like that one Frimpong did is six to nine months."