The Frenchman has not played since retiring hurt against Latvia's Ernests Gulbis during his second-round clash at Wimbledon.
Tsonga, a quarter-finalist in New York in 2011, announced the news on his official website saying the August 26th start date for the US Open is just too soon.
"I have to take care of my health and make sure I can play 100 per cent," he said,
"The thinking is simple, the doctors told me it would be two months for my tendon to partially heal and five months to be completely healed.
"Two months is the amount of time between the injury and the US Open. It would be stupid for me to go there knowing full well that I have no chance because I'm not prepared enough."
Tsonga said he instead hoped to begin his road to full recovery by playing in Metz from 16 to 22 September.
"I know exactly what I have. I know exactly how long it will be before I'm back on top. This is an injury that I've had before," said Tsonga.
"Whenever I've hurt myself before I often come back again even stronger.
"I still have one month (before I play again), it will come soon enough, but I am optimistic!"