It is “un monster”.

I think you can guess by according it to the drink name. Like un soda, un thé, un café, une bière etc.

Using the generic underlying word to figure out the gender is a sound practice indeed. But, I see this as a “boisson énergisante” or “énergétique“, depending; more so (to me) than a soda(m., see also). The word “boisson” is feminine. The specific answer to the question is neither: a capital “M” is still required as this is no common name but rather a brand name. Despite there being ten times more web hits using the masculine (3000 hits with “boire un monster”), I would nevertheless suggest:

Une (boisson énergisante de la marque) Monster.