Harrison, on the disabled list with shoulder inflammation, was diagnosed with thoracic outlet syndrome, which affects the nerves that pass through the shoulder into the neck. The surgery would remove a rib on the left side of his upper chest.
Harrison was 8-3 with a 3.87 ERA in 19 games, including 16 starts, before going on the disabled list June 28 for the second time this season. He experienced tingling fingers during a rehab start with Triple-A Frisco on Wednesday.
Harrison will likely miss the rest of the season if he has the surgery.