The 31-year-old rookie went 9-3 with a 2.81 ERA in 20 starts and 121 2/3 innings. He was on the disabled list from Aug. 8 to Sept. 2 because of right elbow inflammation and was 2-0 with a 1.88 ERA in three starts since his return.
"He finished exactly the way we wanted him to finish coming off the injury," manager Craig Counsell said Saturday.
Broxton will miss the remainder of the season after breaking his right wrist on Friday when he slammed into Wrigley Field's left-center field wall tracking down a line drive. Nieuwenhuis replaced Broxton, then left due to an abdominal strain. He is to be re-evaluated on Monday in Milwaukee.