The 19-year-old, who had been a substitute, was withdrawn just 18 minutes after coming on, appearing in excruciating pain.
Agyemang, known for her role in England's Euro 2025 triumph, received a standing ovation as she left the field at Pride Park.
England manager Sarina Wiegman described the incident as "horrible" and stated it "didn't look good", with teammate Beever-Jones also expressing deep concern.
The injury overshadowed England's otherwise strong performance, which saw goals from Beever-Jones, Lucy Bronze, and Georgia Stanway.