Cartilage piercing in middle of ear was torn out leaving a small tear. Will it require to be stitched up or will it heal itself?

To ensure a meticulous result, any time you have a tear in your ear, it should be surgically repaired, preferablly at the time of the injury. Composite injuries involving skin and cartilage will heal, but if the edges are not approximated exactly, a residual deformity be present.This is a simple fix, typically under a local anesthetic in the office. 

Unfortunately, a torn ear or earlobe heals, but leaves a split that needs to be repaired by freshening the edges of the split and repairing the skin and cartilage in layers.  Fortunately the surgery can be done in the office under local anesthesia.

More than likely this will heal with a split and eventually need to be surgically repaired.  If it was a fresh injury it may partially heal.