Papagiannis was taken from the Cox Pavilion in a wheelchair after he landed hard on his left side and spent an extended period on the ground in obvious pain.
Papagiannis was unable to put weight on his left leg as he was helped off the court by teammates.
Kings summer league coach Jason March said the injury looked terrible when it happened.
Papagiannis, the 13th overall pick in this year's draft, appeared to suffer a cut elbow as well.
ESPN's Kevin Pelton and Ohm Youngmisuk contributed to this report.