The 19-year-old, who is a product of Villa's youth system, has represented the Republic of Ireland at all levels up to Under-19.
Carlisle manager Graham Kavanagh told the club's official website: "He's been on our radar for a while.
"I've watched him play twice and he's a centre forward who knows where the goal is.
"He's looking for an opportunity to show what he can do and we're happy to give it to him. Hopefully he'll get us some goals.
"The key for any player we bring in is that he wants to be here and you can tell that Michael is hungry to play."