I can't verify the quality of these studies but it seems that injury rates per 1000 active hours of crossfit at 0.27 - 0.74 [1] are significantly lower than more common sports such as running at 2.9 - 4.4 and basketball at 6.3 - 12.9 [2]
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6201188/ [2] http://bionics.seas.ucla.edu/education/Rowing/Injury_2004_01...