The Frenchman trailed the world number one 6-4 3-0 last night when he decided he could no longer continue.
However, the 26-year-old has insisted that he will still participate in the US Open, which begins at the end of this month, and could even take part in the Cincinnati Masters next week.
"I've had a pain in my arm for the last three days," Tsonga told reporters after his retirement.
"It was really hard for me to hit the ball well and hard enough so I went and had some ultrasound treatment.
"My arm is fine, it's just tired.
"It will be fine for the US Open and I hope to recover in a couple of days to play in good shape in Cincinnati."
Tsonga will go into the US Open ranked number 15 in the world.