Wawrinka was forced to retire injured after only three games of his semifinal against Bublik when he was losing 2-1 in the first set, walking over to the umpire's chair to announce his withdrawal.
Sonego, meanwhile, recorded a surprise 7-6(5), 6-4 victory over second seed Hurkacz to book his place in the final.
The unseeded Italian won a tiebreak to take the first set before breaking Hurkacz late in the second set and serving for victory on his first match point.
"I'm really happy, because this is my first final this year, and I've played so well day after day," Sonego said.
"I'm really happy for that. Hubi is a great server, and it's very tough to return the ball, but today I played so well and I enjoyed every moment on court."
Sonego will be aiming for his third ATP Tour title when he faces Bublik in the final on Sunday.
Information from the Associated Press contributed to this report.