The short answer is Yes. The long answer below, a piece written by National and Olympic Track & Field Coach, George Van Zyel:
Drs. Holly Benjamin and Kimberley Glow wrote an article Strength Training for Children and Adolescents: What can physicians recommend? published in The Physician and Sports Medicine Vol.31-No.9 September 2003. It provides an honest appraisal of the value of strength training for young athletes and the risks associated with various forms of strength training.
Their conclusion was that the "current published literature demonstrates that the benefits of strength training far outweigh the potential risks." Interestingly, they found that the safest type of strength training involved Olympic Lifting because of the heavy emphasis on proper technique.
As long as the strength training programme is supervised, the answer is a resounding "YES IT IS SAFE" from the following organizations:
American Academy of Pediatrics
American College of Sports Medicine
American Orthopaedic Society for Sports Medicine
British Association of Sports & Exercise Science
Canadian Society for Exercise Physiology
National Strength and Conditioning Association
United Kingdom Strength & Conditioning Association
This is a view of the safety of weight training and particularly weightlifting that is supported by empirical evidence. Brian Hamill conducted a survey involving a number of British schools and published the results in the article Relative Safety of weightlifting and weight training that appeared in the Journal of Strength and Conditioning Research 1994;8(1);53-57. The results appear below:
You can read the full article here.
Strength is the Foundation,