Copper futures fell below $5,000 a metric ton for the first time since the financial crisis, dropping under a key level in a market that has been hit hard by concerns over the Chinese economy and by uncertainty for a metal widely regarded as a barometer of global economic health.

Copper’s decline comes as all metal prices continue their steep falls from the boom peaks of 2011. As with other base metals, copper has suffered from the oversupply that followed the boom and from concern over future demand from China, which consumes...