The move after Saturday's 9-3 win over Pittsburgh came one day after he gave up five runs in one inning to the Pirates.
Brewers manager Ron Roenicke said he doesn't think ''it's anything serious.''
Thornburg is 3-1 with a 4.25 ERA in 27 games.
He had a streak of 13 consecutive scoreless appearances from April 5-29. Since then, he has a 7.80 ERA in 13 games.
Fiers will be used out of the bullpen. He was 6-3 with a 2.53 ERA in 11 starts for Nashville.
The right-hander pitched in 36 games (25 starts) for the Brewers from 2011-13, and was 10-14 with a 4.20 ERA.