Wawrinka, who could play Murray in the semi-finals, had to have treatment to his lower back during his 7-5 7-6 (9-7) 6-2 win on Court One, which ended French hopes of a first male champion since 1983.
The problem for Murray, who saw off eighth-seeded Kei Nishikori 2-6, 6-1, 7-6 (0), 6-1 on Wednesday, is that the man standing in his way is Stan Wawrinka, the 2015 champion.
Murray, who was runner-up to Novak Djokovic at Roland Garros a year ago, will meet 2015 champion Stan Wawrinka for a spot in Sunday's final.
Japanese superstar Nishikori had outlasted Murray in a five-set classic at last year's US Open and looked set to get the better of the Scotsman after breezing through the opening set.
The three semi-finalists, Rafael Nadal, Dominic Thiem and Wawrinka are yet to drop a set this tournament while Murray has lost three, and their build-ups were rather different too.
In windy conditions Murray double-faulted to lose serve in the third game and Nishikori pinged a forehand victor past him to move 5-2 ahead before serving out the set.
Romania's Simona Halep dismissed 21 seed Carla Suarez-Navarro 6-1, 6-1 to reach the quarterfinals on the women's side. The Serbian tennis star is still in action at Roland Garros.
Asked about his chances of going on to win the French Open, a major that has hitherto eluded him, Murray said: "I probably need to play better than I did today, but you never know".
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Asked if he had given any ground to Britain, Mr Barnier said: "I am not in a frame of mind to make concessions, or ask for concessions".
Djokovic was thumped 7-6, 6-3, 6-0 by the Austrian in the French Open quarter-finals.
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"I don't know how I get the second and third".
"It will be tough but I'll fight as hard as I can. It doesn't keep me from playing, and it doesn't keep me from playing well", Wawrinka said about his back. He's been playing very well.
The seventh seed pair shocked third seeds Andrea Hlavackova and Edouard Roger-Vasselin 7-5 6-3 in the semifinals. Stan this tournament has played great.
Wawrinka demolished Marin Cilic 6-3 6-3 6-1 while Nadal has lost just 22 games in five matches after opponent Pablo Carreno Busta retired with an abdominal injury when trailing 6-2 2-0. In another quarterfinal, Pliskova meets No. 28 Caroline Garcia, a 6-2, 6-4 victor against Alize Cornet in a match between two Frenchwomen.
Nishikori said: "We have been playing so many times".
The third-seeded Halep, who trailed 5-0 in the first set, was down 5-1 in the second. "It's always nice to see him play well".
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