If the tear is small and doesn't cause swelling, you may be safe to exercise. But exercise probably won't fix the tear. This is because joint cartilage does not have its own supply of blood and lymph vessels. This means the cartilage is not able to heal on its own. If the tear goes all the way down to the bone, you may not require surgery. But again, your knee will probably not get better as a result of doing exercise.
It's best to choose exercises like swimming or biking, to keep from forcefully jarring the joint and putting extra pressure on the unprotected portion of bone below the tear. If the cartilage and the bone below it have become unstable or dislodged, exercise will make things worse, meaning surgery will probably be recommended.