Burdisso was sent off for the tackle in Roma's 5-1 defeat.
Cagliari coach Pierpaolo Bisoli said: "Conti is upset about the injury, but still happy, as with no fractures it is effectively less serious than we originally thought.
"It is a very deep cut to his knee and shin. We'll see now what the test results say about potential ligament damage. Hopefully we can have him back in three weeks.
"We all feel bad, as Daniele is an important player and was having a great game, even scoring the first goal. Unfortunately these things happen in football. We can only hope it's just a cut and there are no further complications."