The former England international had to be substituted after 16 minutes of the game in Denmark following a challenge with Thomas Augustinussen.
Ryan Giggs came on as his replacement, and Scholes could now face a lengthy lay-off.
Manager Sir Alex Ferguson confirmed on ITV4: "He's got knee ligament damage.
"We don't know how serious it is obviously.
"We'll have it assessed as soon as we get home."