To start with we don't know whether the universe is infinite or finite but unbounded (i.e. closed on some length scale much larger than the visible universe). If the universe is infinite the amount of matter is probably also infinite, while if the universe is finite the amount of matter is definitely finite.
Also when you say "matter", you need to bear in mind that matter is being converted into energy in stars, so it would be better to ask about combined matter and energy, where we treat the two as the same and link them with Einstein's famous equation $E = mc^2$.
Having made these two points, with one exception we know of no mechanism for matter/energy to appear from nothing i.e. the amount of matter/energy is conserved. In fact this conservation law follows from a fundamental symmetry that the laws of physics are time invarient. So whether the universe is infinite or finite, the amount of matter/energy in it is constant with time.
I did say there was one exception: you've probably heard of dark energy, which is a fundamental property of spacetime. The thing is that because the universe is expanding the amount of spacetime is increasing and therefore the total amount of dark energy is increasing. Since we don't know much about dark energy, it's hard to comment on the significance of this.