Since the carcinogenic effect of asbestos is mostly caused by it's physical properties[1]; anything that resembles the shape of asbestos' micro-particles is also highly suspected to be carcinogenic.

The shape, size, and adsorbing nature of the fibers also appear to be critically important. Recently, doubts have arisen concerning the safety of commercially available carbon nanotubes,[2] which may possess the same carcinogenicity as asbestos fibers because of their similar characteristics. Ample care has to be taken to prevent a tragedy similar to the one caused by asbestos exposure.[1]

[1] http://www.med.nagoya-u.ac.jp/medlib/nagoya_j_med_sci/7112/p... [PDF]

[2] http://www.nature.com/nnano/journal/v3/n7/abs/nnano.2008.111...

On making nanotubes less dangerous: Shorter is better http://onlinelibrary.wiley.com/doi/10.1002/anie.201207664/ab...