That is actually a really cool and unexpected question!
MMPs are produced when there is a need for them (well, duh!) -- basically, when there is tissue inflammation of some kind. In this case, the inflammation is in the tendons, and hence there is remodeling that comes after the inflammation. MMPs are produced by such immune system cells as granulocytes and lymphos, primarily T-cells that have been activated.
As far as their tissue inhibitors (TIMPs), I am pretty sure that they are produced in numerous cells and locations.