SYDNEY—The price of silver surged to a two-year high on Monday as buyers in China made bold bets in the futures market and scooped up vast volumes of physical metal.

Spot silver, the price paid for immediate delivery, rose as much as 6.9% to an intraday peak of $21.132 a troy ounce, its highest value since July 2014, as the Shanghai-traded benchmark futures and physical silver contracts reached their limit.

On...