Hahn was set to start Tuesday night against the Pittsburgh Pirates.
The right-handed Hahn was 2-1 with a 2.20 ERA in 10 games at San Antonio.
The Padres also selected left-handed pitcher Jason Lane from Triple-A El Paso. He Lane was 5-4 with a 4.36 ERA in 11 starts.
Padres starter Eric Stults was placed on the bereavement list and will miss between three and 10 days. He is 2-6 with a 5.03 ERA.
The team also optioned right-hander Donn Roach to El Paso after he went 1-0 with a 4.75 ERA in 16 games.