Is there any prohibition against a man walking with his hands clasped behind his back?

There is no harm in a man walking with one hand grasping the other behind his back. The basic principle regarding customs is permissibility, unless there is evidence to the contrary.

However, if this manner of walking is considered blameworthy by people of integrity and respected stature in a particular society, then the custom of the people should be observed, and this manner of walking should be abandoned to preserve one's integrity and to protect oneself from gossip and idle talk, as was done by imams such as Al-Ahnaf ibn Qays and Imam Al-Shafi'i.