The former top-ranked Dane squandered a 3-0 lead in the first set and never recovered after losing the tiebreaker.
Also, fifth-seeded Petra Kvitova of the Czech Republic beat wild-card entry Annika Beck of Germany 7-5, 6-7 (0), 6-3. She broke serve for the second time in the final set for a 5-2 lead.
Barthel said she was tired after helping Germany defeat Serbia in the Fed Cup playoffs for a place in the World Group.
Julia Goerges of Germany, who beat Wozniacki for the 2011 title in Stuttgart, advanced to the second round when Kirsten Flipkens of Belgium retired with stomach problems. Goerges was leading 6-2, 2-1.