World No 1 and 2010 champion Novak Djokovic was also forced to pull out because of a back injury.
Croatian Marin Cilic beat South African Kevin Anderson 7-6 4-6 6-1 and Berdych thrashed Spaniard Fernando Verdasco 6-1 6-0.
Frenchman Tsonga predicted a battle of wills in Saturday's showdown against world number 10 Berdych.
"I'm really happy. Tomorrow will be exciting for sure as we both have a lot to win to be safe for the Masters Final (in London)," said the world No 7. "Both of us will play our best tennis to win the match."
Ivan Ljubicic also reached the last four with a 7-6 6-7 6-2 win over Mikhail Youzhny.