Karolina Pliskova, the second seed, claimed a marathon first set on the way to beating the last French player remaining in singles, Caroline Garcia, 7-6 (7-3) 6-4.
Nadal reached his record 10th French Open semifinal when fellow Spaniard Pablo Carreno Busta retired from their match early in the second set because of an injured abdominal muscle. "Just pretty bad set".
He quickly moved 3-0 ahead in the second set and, although Djokovic initially showed some fight, it soon drained away.
"The past few months, I have been playing very well", said Nadal.
Download the Nigeria Today app from Play store. "It's a big challenge, but I'm up for it", added Djokovic.
Thiem is the only player to have beaten Nadal on clay this season, but the 23-year-old is under no illusion about the size of the task that awaits him in Friday's semi.
Calabar agog as Acting President Osinbajo visits
The Federal Government has pledged full support for the proposed Cross River 275km Super Highway and the Bakassi Deep Seaport. Acting President Yemi Osinbajo has arrived Cross River for a one-day visit to the state.
Thiem breezed past the Serb 7-6, 6-3, 6-0 to book his place in the semi-finals and send the defending champion packing. Their last meeting on that surface was in last year's French Open semifinals, a four-set win for Murray. I have to get through it and learn the lessons and come back stronger.
The title favourite, who has gone on to lift the trophy the other nine times he has made the last four, has lost just 22 games in five matches so far.
"It happens to almost all players, at some point in your career you're going to go a little bit flat, you're fighting with yourself, you're not making the right choices, you have to think about everything, you're not feeling anything and I think he was trying to do too much with his backhands, he missed a lot of backhands".
"I have never had any issues with him before", Murray said.
The second-seeded Djokovic had two set points in the opener but couldn't convert either. Murray advanced to his fourth straight semi-final in Paris, defeating Nishikori to avenge his loss to the Japanese star at the US Open a year ago.
Wawrinka improved to 12-2 career against Cilic.