He suffered the injury while playing for the Australian national team. The team was playing the Slovenia national team in Ljubljana, Slovenia, on Tuesday.
Exum was driving into the paint and came to a jump stop in the middle of the lane when his left knee buckled. He was untouched, but went down as he lifted for the shot.
"First and foremost, our overriding concern is with Dante and his long-term health," Jazz general manager Dennis Lindsey said in a statement.
"We are continuing to work closely with our medical staff, Dante and his representation in order to reach an accurate diagnosis and recommended treatment so that we can provide him with the best possible care. We all know how hard he will work to make a full recovery and look forward to his return to play."
Exum was drafted by the Jazz with the No. 5 pick in 2014 and started 41 games. He averaged 4.8 points and 2.4 assists and was expected to make significant advances to his game this summer.
The Associated Press contributed to this report.