Hill had previously been ruled out for his start Sunday against the Cleveland Indians after saying the blister on his left middle finger hadn't fully healed.
Sonny Gray will start in place of Hill on Sunday.
Hill, who left his last start July 17 after only five pitches because of the blister, said the finger is feeling better but that it began to feel "hot" after he threw a 60-pitch bullpen session Friday, according to the San Francisco Chronicle.
"It feels like we're making good progress, but if we run out there and end up in a situation like we were last time, we're pushing it back even more," Hill told the Chronicle. "We're already at two weeks at this point."
Hill is 9-3 with a 2.25 ERA and has 90 strikeouts and 28 walks this season.