Scores are only good for 3 years, and some schools will say something like "No scores later than January 1, 20xx." So even if you take the MCAT in September 2020, schools might still say that your score will be invalid to them after January 1, 2023 rather than September x, 2023. It's something to keep in mind.
With that said, you could still apply to medical school while in your master's program, which can help you get an application in before your score comes very close to expiration. Schools will expect you to finish the master's program by the start of classes, though.
I suppose you have to ask yourself if you would have nothing to do over the summer before the master's program starts. It wouldn't hurt to have it done while you have no other major obligations that way you don't have to worry about juggling the MCAT prep and the master's at the same time. It's more efficient use of your time. Now, if you aren't getting your target score by September 2020, delay that MCAT and just do a little bit of MCAT prep each day while in your master's (but not at the risk of doing poorly) until those MCAT practice scores get close to target.