World number seven Thiem advanced to his first semi-finals at Indian Wells without hitting a ball after Monfils' withdrawal.
Thiem has lost both of his prior matches against Raonic, who ended the dream run of lucky loser Miomir Kecmanovic, beating the 19-year-old Serbian 6-3, 6-4.
The Canadian will face Thiem for a place in the final after the seventh seed's quarterfinal opponent Monfils said he was unable to play due to an injured Achilles.
"I would like to thank you for everything you gave me this week and again I'm sorry".
From 4-2 down, the World No.8 ran off the last four games of a high-quality opener which saw almost 20 winners combined between the two players, and Kerber broke the No.23 seed for the third time from 30-0 down in the set's last game. "I have this pain, and it wasn't the right choice to play".
Belinda Bencic beat fifth-seeded Karolina Pliskova 6-3, 4-6, 6-3 to reach the semis, ensuring her return to the top 20 in the rankings. "She has nothing to lose, she enjoys her tennis and she's a great player", Kerber said of the teenager.
Despite appearing in her first Premier Mandatory final, the 31-year-old will contest her 29th WTA final overall against the Canadian wildcard in their first-ever meeting. "I think that can get better".
"I was really surprised", Thiem said, who was waiting to be taken to the court when he realized there was a problem".
In the victory, Kerber won 65 percent of her first serve points and 68 percent of her second serve points. From the get-go, Kerber made strong in-roads into Williams' serve, especially the second serve and was just as relentless on her own serves.
Raonic is looking for his ninth career ATP Tour title, but has never won at the top level below Grand Slams - Masters 1000.
Bencic was pushed to three sets for the first time in four matches at the tournament. She's here as a wildcard, and she beat a lot of good players.
"When you're confident, you can really just trust your instincts and you don't have to think about it at all", Bencic said.
Canada's Bianca Andreescu will meet sixth seed Elina Svitolina of Ukraine in the other Indian Wells semi-final.