Henrik Rung (March 30, 1807 – December 12, 1871) was a Danish composer.

Rung received training with the Royal Danish Orchestra in Copenhagen.

He received a travel grant to study in Germany, Italy and Paris (1837-1840).

In 1842, Rung became a singing master and held a lifelong position as a director of the opera at the Royal Danish Theatre.

His son Frederik Rung (1854-1914) was also a composer and his daughter Sophie Keller (1850–1929) was an opera singer at the Royal Danish Theatre.