I can't speak specifically to matchlock muskets as you've asked, but I can speak to the Brown Bess flintlock musket which should in part answer your question. The Brown Bess typically wasn't assembled all by one person, or even in one place, given the different skills needed to produce a single weapon.

The lock (the firing mechanism) would be assembled by a gunsmith (Grice, Willits, and Baker being some of the more well known). This was the part of the weapon that involved the most skilled labour, and also had the longest turnaround time to produce, given the number of fine moving parts. The barrel was somewhat easier to produce, as it involved rolling and welding a sheet of iron into a tube. The stock was by no means easy to produce, as the wood had to be carved to match up to the metal parts and also not split when subjected to the stresses of firing.

The three components would be shipped to the Tower of London and assembled there before being issued to individual British regiments. This is also where we get the expression "lock, stock, and barrel" meaning to have everything, as those are the three components needed to assemble a musket.

So, to sum up, weapons like the flintlock weren't actually "mass produced" per se, but required the coordination of many craftsmen. This of course had drawbacks, such as the difficulty of ramping up production during times of emergency. As well, centralization could pose its own issues. For example, a fire at the Tower in 1841 destroyed large numbers of Brown Bess muskets awaiting conversion from flintlock to percussion ignition.

Source: Anthony D. Darling, Red Coat and Brown Bess.