Hi, you mentioned "thickness tear", you missed the most critical word - I assume you've taking x-ray or CAT scan, from the imaging Radiologist will write down "full-thickness tear" or "partial-thickness tear".
The treatment to supraspinatus muscle tear depends on the severity. A partial-thickness tear is an incomplete disruption of muscle fibers, the muscle fibers may heal on their own over time, so the Orthopedist will give you anti-inflammatory drugs, and ask you to rest your arm and shoulder. A full-thickness tear means the complete disruption of the fibers of the supraspinatus muscle, they generally require a more aggressive treatment plan and surgery. These tendons have poor blood flow and can't heal themselves. If the tendon had separated from the bone, it will be attached to the bone with sutures in a surgery.
If you may check your x-ray report again, see it's a full-thickness tear or not. A full-thickness tear requires a surgery to repair.