Monfils, a wild-card entry at the Austrian event, will next face fourth seed Lleyton Hewitt after the Australian demolished Argentina's Diego Hartfield 6-2 6-2.
Second seed Roddick, looking to improve on his clay court form ahead of next week's French Open, had appeared in total control after breaking his 20-year-old opponent to go 5-4 up in the first set.
Monfils, a three-time junior Grand Slam champion, broke back in style however, levelling the scores with a great reaction volley at the net.
Another well-timed run to the net two games later helped the Parisian break Roddick a second time to complete an unlikely first set comeback.
Roddick had his own opportunity to fight back at the start of the second set when Monfils hit three successive forehands long to trail 0-40.
The Frenchman saved all three break points with an ace, a deft backhand volley and a perfectly-struck forehand winner, and was soon reapplying the pressure on Roddick, breaking the American once more to go 2-0 ahead.
Losing his cool in the Austrian heat, the 2003 US Open winner smashed his racket in the following game before hurling a string of abuse at himself.
The outpouring had little effect though with Monfils holding his serve for the rest of the match to complete a second successive win over Roddick following his 6-2 6-3 win at the quarter-finals of last year's Masters Series in Rome.
Hewitt was never in any danger of a similar upset during his match against Hartfield, breaking the world number 97 five times to set up his semi-final encounter with Monfils.
The Australian, who reached the last four in Hamburg last week, has now made it to two successive clay-court semis after a previous three-year drought.
(Writing by Mark Ledsom in Berne)