The Finland international signed a six-month deal in August of last year when Mark Ridgers suffered a long-term injury.
But Enckelman only made one appearance for the Jambos, coming off the bench during a 1-0 loss at Celtic in October when Jamie Macdonald was stretchered off.
The Hearts website said: "The club would like to thank Peter for his efforts during his short spell here in Gorgie, and wish him all the best for the future."
The 35-year-old Enckelman has been capped 12 times by Finland and, prior to joining Hearts, he had spells with Aston Villa, Cardiff and St Johnstone.
Another Hearts goalkeeper, Jack Hamilton, will remain on loan with Forfar until at least 12 February.