I’d say lower than most other contact sports, since it’s focused on the ground game. In over a year of going 3-5 times a week, I think I’ve had one or two tweaks that bothered me for more than a couple of days. I’ve been injured far worse playing ultimate frisbee for Navy PT. (3 cracked ribs… it was a competitive game)
Lifting, running, BJJ, and other sports all present a so-called “risk of injury”. Being out of shape and getting shin splints or tweaking your “bad back” because you’re weak and out of shape is a far bigger risk IMO, nevermind the heart issues and other health risks from being overweight and/or out of shape. Pick your poison…