http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4780097/
This 2013 study by Dodson et al. reviewed ACL tears in the NFL in order to see if there were any trends. I've attached a screen shot from Table.4 of the study and as you can see, ACL injury rates are nearly the same on grass and artificial turf. No statistically significant findings.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4820027/
Another study that was just released a few months ago that aimed at identifying extrinsic risk factors for injuries. They found that playing surface had no significant effect on concussions, hamstring injuries, ankle injuries, knee injuries, but they did note that playing a team game on grass actually increased the risk of shoulder injury.
"anecdotal evidence and player reports suggest poor footing on newly sodded soft grass surfaces27 potentially increasing the risk of falls and shoulder impacts."
The only solid association this study found was cold temperature correlating to concussions and ankle injuries.