The fifth-seeded German lost 6-4, 6-2 to an 18-year-old Roland Garros beginner, Russian Anastasia Potapova, on Court Philippe Chatrier.
German player Angelique Kerber is in third place, while Dutch player Kiki Bertens climbed from seventh to a career-high fourth position after beating Halep on Saturday in the Madrid Open.
Kerber had been struggling to recover from a protracted bout of flu and confirmed that she was under doctor's orders not to play this weekend.
The 18-year-old was ranked No.60 coming into the tournament but will now rise to 24th following his maiden WTA title.
After toppling Elina Svitolina in three sets, Canada's Bianca Andreescu will face Wimbledon champion Angelique Kerber for the title.
The world number 44 beat Stephens 6-7 (3/7), 6-3, 6-3 to set up a last eight clash with another American, Danielle Collins who knocked second seed Angelique Kerber.
Collins humiliated the German three-time major champion 6-0, 6-2 in less than hour to reach the quarter-finals on her debut appearance in the Melbourne Park main draw.
The second-seeded German was made to work hard in the opening set against Italy's Camila Giorgi, but took control in the second to ease through 7-6 (7/3), 6-2.
To win the decisive tie-break, a player will need to be the first to 10 with an advantage of at least two points.
Hopman Cup is widely tipped to be scrapped to make way for the new ATP World Team Cup, which will start next year.
Switzerland took its fourth Hopman Cup title overall when Federer and Belinda Bencic beat Alexander Zverev and Angelique Kerber 4-0, 1-4, 4-3 (4) in the Fast4 format in the mixed doubles decider.
Former coach of Kim Clijsters, current world number one Simona Halep and Victoria Azarenka, Fissette joined forces with Kerber in November 2017.
World number three Kerber has already qualified for next month's Finals which will be held in Singapore and advanced after a knee injury forced her American opponent Madison Keys to retire.
While Serena was frustrated by the surprise setback, she took heart from her run to the final in just the fourth tournament of her comeback following daughter Olympia's birth in September.
Williams had hoped to equal Margaret Court's record of 24 Grand Slam singles titles by winning her first major prize since becoming a mother in September.