Djokovic, the 36-year-old world number one came through a rollercoaster quarter-final to win 7-5, 6-4 and make the last-four in the principality for the first time since 2015 when he went on to claim his second title at the tournament.
Djokovic, the oldest man to make the Monte Carlo semi-finals in the Open Era, will take on either Casper Ruud of Norway or France's Ugo Humbert for a place in Sunday's championship match.
"It was tough for both of us. He is one of the quickest players on tour. He gets a lot of balls back that normally 99 percent of other players don't," said Djokovic who avenged his loss to De Minaur at the United Cup in January.
"He did not surprise me with several passing shots. Particularly in the second set when I was up a break.
"But he said at the net it was ugly. The second set I think it was. We didn't play at the high level and made a lot of unforced errors, him and I, and a lot of breaks of serve. It is kind of expected on clay but maybe not this many. But a win is a win and I am happy to be through."
Saturday's other semi-final sees Australian Open champion and world number two Jannik Sinner face two-time Monte Carlo winner Stefanos Tsitsipas.
Sinner took his 2024 record to 25 wins and just one loss with a gruelling 6-4, 6-7 (6/8), 6-3 victory over 2023 runner-up Holger Rune.
Greek 12th seed Tsitsipas breezed past Karen Khachanov of Russia 6-4, 6-2.
Djokovic had appeared on course for a comfortable afternoon under the sweltering Riviera sun against 11th seeded De Minaur.
After pocketing the first set, he was quickly 2-0 ahead in the second.
However, five successive breaks of serve followed as the top seed saw leads of 3-1 and 4-2 retrieved by his opponent who clawed back to 4-4.
Djokovic held for 5-4 and secured his fifth break of the match in the 10th game to claim victory in just over two hours and move two wins away from a 41st career Masters title.
Sinner kept his cool as Rune lost his in a two-hour 40-minute marathon.
Rune, who will drop out of the top 10 next week, was warned by the chair umpire for unsporting behaviour after a sarcastic gesture to the crowd in the second set.
Rune 'chaos'
He was booed even more when he sat down and demanded the supervisor be called.
The 20-year-old Dane regained his composure, saving two match points to take the tie to a decider.
However, Sinner moved smartly into his fifth semi-final of 2024, gaining revenge for his loss to Rune in the last-four in Monte Carlo 12 months ago.
"One can try and create a little bit of chaos," said Sinner of Rune's antics.
"That is no problem. I learned from last year. That is all part of the learning process."
Tsitsipas, winner of the Monte Carlo title in 2021 and 2022, needed just 81 minutes to record his eighth win in nine meetings against Khachanov.
"I was very effective from the start, I had a lot of pace and gained momentum," said Tsitsipas.
"I tried to do my part and press and it worked out really well."
Tsitsipas added: "There are many good memories here and stepping out and coming back revives those good memories. It brings me alive."
