The top seed needed one hour and 27 minutes to wrap up a straightforward 6-4 6-1 triumph over the Swiss at WTA International clay-court event on Friday.
Radwanska set her stall out early by taking a 2-0 lead, but she was quickly pegged back to 2-2.
Another break apiece took the score to 3-3, but from there the Pole exerted her dominance and won eight of the next nine games to take a 6-4 5-0 lead and, though she was broken when serving for the match, was able to break Meusburger for the win.
"The court was a bit different from that in the first two matches," Radwanska said after sealing her last-four berth.
"It took some time before I got used to it, but the most important thing is that I got through."
Awaiting the world number three is France's Alize Cornet, as the fourth seed came through a back-and-forth encounter with fifth seed Klara Koukalova 6-2 0-6 6-2.
Elsewhere, Italy's Camila Giorgi needed less than an hour to see off the challenge of Israeli Shahar Peer in a 6-1 6-4 triumph.
And she will meet third seed Carla Suarez Navarro in the last four, after the Spaniard defeated Magdalena Rybarikova 6-2 6-3 in Friday's last quarter-final.