Everything that's physically challenging carries the chance of injury. Deal with it.
Running risks joint degeneration. Bicycling can be bad for sexual function and mobility. Hikers get lost and freeze to death. Tennis causes elbow pain. Soccer players blow out their knees. Baseball players risk concussions from wayward pitches to the head. Lifting weights can cause spinal injurymuscle pulls and ligament tears. Sex causes pregnancy, STDs, and feelings. Anything strenuous risks heart attacks, strokes, muscle pulls and joint injury. I can't think of any exercise that doesn't have risks. But--sitting on the couch causes diabetes, heart disease, immobility, boredom, and a boring personality.
"Martial arts" is too broad a category to define risks for. The risks are totally different between two karate schools, because one is hard contact and the other is no-contact. Aikidoka and BJJ practitioners both experience accidental joint and soft tissue damage, it's just a question of which joints are more common to get hurt.
If injury prevention is a high priority, then you shouldn't train any sparring arts, nor anything that involves joint locks or drilling with contact. You'd be better served going to a gym and developing a maximum-safety running-and-lifting program. But if you want to learn a martial art, then recognize that all activities carry risks, get over it, find a place to practice where people aren't meatheads and they clean the mats regularly, and start training instead of thinking about it.