Djokovic, who led 6-4, 3-0 when Tsonga retired, will face sixth-seeded Mardy Fish on Sunday.
"I don't think my game will significantly change," Djokovic said about Fish's serve-and-volley game. "I will play the game I always play -- aggressive from the baseline, trying to take every chance to go for the shots.
"But there are different tactics with every player. Mardy is one of the rare players that plays serve and volley nowadays. I think these conditions, which are a bit faster, are quite suitable to his style of game. He's been winning his matches quite comfortably. He's been serving extremely well."
The Australian Open and Wimbledon champion playing his first tournament since taking the top spot in the world ranking, Djokovic improved his match record for the year to 52-1, including 28-0 on hard courts.
Djokovic, the Rogers Cup winner in 2007, is seeking his ninth tournament win of the year and his record fifth of the season in an ATP Masters 1,000 event.
Tsonga, who took Djokovic to four tight sets in the Wimbledon semifinals, indicated to the chair umpire there was a problem with his arm after losing his first service game of the second set.
After Djokovic held service despite his first sloppy game of the match that went twice to deuce, the Frenchman was examined by a doctor at courtside and decided to stop playing.
Tsonga said an ultrasound showed no tear in the muscle, but he was unable to continue. He said the arm had been hurting for three days but he opted to play on. He hopes it will heal in time for a tournament next week in Cincinnati and, if not, by the U.S. Open at the end of the month.
"The pain was worse day after day, hour after hour, on the court," he said. "You know, I don't have the pretension to try to beat Novak without my arm."
The crowd in the packed grandstands at Uniprix Stadium booed, but then cheered lustily for Djokovic, who had made several spectacular shots as he dominated his service games against the hard-hitting Tsonga.
Earlier, Fish advanced to his third straight ATP Tour final, beating Janko Tipsarevic 6-3, 6-4. Fish has won 11 of his last 12 matches, winning at Atlanta last month and reaching the final two weeks ago in Los Angeles. He's trying to become the first American to win the Rogers Cup since Andy Roddick in 2003.
"I win a lot of matches because I can play a lot of different styles, I think," the 29-year-old Fish said. "A faster surface like this is going to suit my game perfectly -- a hard court where I've got my footing pretty good. My serve moves through the court well. You can come in. You can stay back a little bit, as well. But to be this successful, I have to play really well, too, and I've done that."
Djokovic beat Fish 6-3, 6-1 in their last meeting in Florida in March.
"Conditions are different," Djokovic said. "In Miami, the bounce is (higher) than here, it's slower than this surface. I've been playing night matches, he's been playing day matches. Tomorrow we play (at 3 p.m.). Maybe it's going to be hot.
"It's important when you play a player like Mardy to hold your composure, to be patient and wait for the chance on his service games, try to have high percentage of the first serves and stay aggressive. I know he's going to come to the net. I know he's going to take his chances. He's always played like that."
In the doubles semifinals, top-seeded American brothers Bob and Mike Bryan beat Tomas Berdych and Floridan Mayer 6-2, 6-1, and Michael Llodra and Nenad Zimonjic topped Daniel Nestor and Max Mirnyi 6-3, 6-4.