Can a meniscus tear heal on its own?

Yes, it can, BUT it-: Is rather unlikely, as they generally don't, unless the tear is a minor one. I don't think they heal but they certainly become symptom-free. Surgery can help certain types of the tears by repairing them which are dependent on the specific site they occur in. Most are however not amenable to repair.

Rarely.: Much of the menisci do not have a blood supply, thus cannot heal. The only ones that have a chance of healing are the tears on the periphery of the meniscus, where there is a decent blood supply.