The operation will be performed in Dallas by Cowboys head physician Dr. Daniel Cooper.
Parker started all three games of a weekend series against the St. Louis Cardinals.
The 33-year-old Pence is batting .298 with seven home runs and a team-leading 36 RBIs. He was placed on the 15-day disabled list after feeling the right hamstring pop while running to first on Wednesday.
Earlier in the weekend, Pence was told he had a 50-50 chance of returning if he skipped surgery and just did rehabilitation work, but if he did that and re-injured himself, the recovery time would be longer.