Argentinian Monaco won the first edition of the ATP 250 event last year but will be unable to add to that success after falling to Karlovic on the clay.
The Croatian - seeded seventh – hit 19 aces in an excellent 6-4 3-6 6-3 triumph.
Karlovic was on form from the off, winning 21 of 25 points on first serve and hitting six aces in the opener to seize the initiative.
Monaco upped his own serving in the second set and claimed the all-important break to force a decider.
But Karlovic ultimately proved too strong, losing just one point on his first serve in the third and final set in addition to another eight aces.
He will play Jiri Vesely in the last four after the Czech thrashed Austrian Jurgen Melzer 6-1 6-1 in just 63 minutes.
Melzer was poor on serve and that allowed Vesely, ranked 104th in the world, to dominate, as he made five breaks en route to a big win.
Top seed Philipp Kohlschreiber was left in the dark – literally – on his progression after his match against Croatian Mate Delic was suspended.
Kohlschreiber led 7-5 4-4 when the game was halted due to darkness.
Awaiting the winner is Uzbek Denis Istomin, who surprised third seed Andreas Seppi of Italy 6-3 6-4.