The top seed appeared sluggish against Switzerland's Voegele, who claimed her biggest win in five years with a 6-4 5-7 6-2 victory.
Stephens started the quarter-final proceedings with errors on her backhand, giving Voegele the opportunity to break in the final game of the first set.
The American showed more aggression in the second, winning the last three games in a row to take the set, but she faltered in the decider as the Swiss dropped just two points in four games.
