Tsonga lost 7-6 (7-3) 3-6 7-6 (7-5) to unseeded Croatian Dodig on Thursday and injured his finger after slipping in the final set.
“I think it’s serious,” said Tsonga after his third-round loss at Queen’s Club. “I felt like I broke something or I stretched ligaments.
“It sounds very bad [but] at the moment I don’t know what it [the injury] is, so I will stay positive and I will see.”
The 27-year-old, who was the second seed at Queen’s Club, will now undergo a scan to assess the damage.
Tsonga, who memorably came back from two sets down to defeat Roger Federer in the Wimbledon quarter-finals last year, lost to world No1 Novak Djokovic in five sets in the last eight of the French Open last week.
MORE: The latest football news
MORE: The latest tennis news
BIOGRAPHY: Daniel Sturridge
BIOGRAPHY: Kepa Arrizabalaga