The Iranian top flight club was without a coach since Abdollah Veisi stepped down from his role in mid-December.
Schafer, 73, had previously led another Iranian side Esteghlal from 2017 to 2019, where he won the Hazfi Cup in 2018 with the team.
Sanat Naft is 14th in the 2023/24 Iran’s Persian Gulf Pro League (PGPL) table, one point above the relegation zone.
AMK/TT