Finnegan was the 17th overall pick in last year's draft. He had a 1.29 ERA in seven regular-season appearances with the Royals in 2014, and then went 1-1 with a 10.50 ERA in seven postseason games.
The 22-year-old Finnegan was 0-1 with a 3.86 ERA in two starts with Northwest Arkansas at the time of the promotion. Royals manager Ned Yost said Finnegan will work as a reliever with the major league club.
Kansas City used five relievers in a 13-inning victory at the Chicago White Sox on Thursday night.
The Royals also optioned infielder Orlando Calixte to Triple-A Omaha on Friday. Calixte was hitless in two at-bats for the Royals.