103rd-ranked Peterson started the match strongly, immediately breaking the Chinese's serve in the first game, 40-15, and then was able to win her own serve point 40-30.
When Rebecca Peterson then again broke Zhang's serve, 40-15, Zhang withdrew from the match and the WTA 1000 tournament in Indian Wells, USA.
The exact reason for Zhang's withdrawal has not been communicated.
After playing for less than a quarter of an hour, Peterson could thus advance to the third round, where she will face 39th-ranked Jil Teichmann.
The Swiss knocked out world number nine Belinda Bencic in the second round.
The top players advanced
In the other matches from Indian Wells, world number six Coco Gauff was able to advance on home soil after knocking out the Spanish Cristina Bucsa (ranked 90) in two straight sets, 6-2 and 6-4.
If both Gauff and Peterson advance from their matches in the third round, they will face each other in the round of 16.
And Greek world number seven Maria Sakkari defeated 41st-ranked American Shelby Rogers 2-1 after turning around a deficit (2-6, 6-4, 6-0).
In the third round, Sakkari faces Ukrainian Anhelina Kalinina, ranked 29th in the world.