The Scot took the first set on a tie-break, but was unable to build on his lead as his Czech opponent hit back for a 6-7 (4/7) 6-2 6-3 victory after nearly three hours on court.
Berdych will now face either world number one Novak Djokovic or Robin Haase in the semi-finals.
Murray and Berdych had met just once before on clay in five previous meetings, with the latter securing a convincing win at the 2010 French Open.
There was little to separate the two players early in the opening set in Monte Carlo, but Murray's second serve then began to let him down and Berdych found himself with the first break points of the match in the eighth game.
Murray saved the first with a drop shot, before Berdych wasted the next two with a forehand and a backhand into the net.
The Scot then faced five more break points in game 12 as Berdych looked to claim the set, but the Czech failed to take any of them and a tie-break ensued.
This time it was Murray who had the mini-break to open up a 6-2 lead. And the third seed gained the advantage on his third set point with Berdych hitting a return long.
Berdych came back strongly at the start of the second set, though, and finally claimed his first break of the match in the third game when Murray put a weak forehand into the net.
And a further break followed for the Czech four games later, when another poor shot from Murray gifted Berdych a 5-2 lead before he served out his next service game to level the match.
Murray was looking slightly deflated now, and it was no surprise when his opponent broke again in the opening game of the third set.
The third seed responded by gaining his first break point of the match in the next game and a wide forehand from Berdych levelled things up.
But Murray's serve continued to let him down and his Czech opponent got his nose in front once more in the third game following another error from the Briton.
Murray fought hard to get back into the contest, but his confidence appeared to be down and Berdych wrapped up another break, and the match, with a winning forehand down the line.
Berdych told Sky Sports 1 afterwards: "It was another tough but really good match.
"It's tough to say what was key. I'm trying to play my game, trying to play aggressive. That's key for my game and if it's working I have the game to beat anybody, even Andy.
"The win over Andy gives me a lot of confidence for the next match."