The third seed, who won the title back in 2023, served brilliantly throughout on the speedy Dubai court, making 83% of first serves and winning 77% of points when landing them.
Brooksby himself had a first serve percentage of 78%, but was unable to get as much joy, winning just under half of them.
The Russian has looked in ominous form this week and is yet to drop a set. He will now face either top seed Felix Auger-Aliassime or Jiri Lehecka in the last four.
Medvedev got off to a rapid start, breaking the American in the first game to put down an early marker. He then whizzed through his service games before getting another break towards the end of the set to take the opener.
The second set was one-way traffic, as Medvedev broke three times to seal the win in just under an hour.
