The truck skidded off the road and fell into the gorge near Pappad Morh in Samba district, about 75 km from here, late Thursday.
The injured have been shifted to hospital for treatment, a police officer said.
Last year, 107 pilgrims had died due to natural causes during the Amarnath Yatra. In 2010, the number was 78 and in 2009, the toll of those dying from natural causes was 42.
About 750,000 pilgrims visited the high altitude cave shrine dedicated to Lord Shiva last year. The figure was 600,000 in 2010 and 450,000 in 2009. This year, 580,000 pilgrims have so far performed the Yatra.
The Himalayan cave shrine is at a height of 13,000 feet and houses an ice stalagmite seen to be an icon of Lord Shiva.