Burr (shoulder) struck out two and worked around two hits to turn in a scoreless inning of relief Saturday in Triple-A Lehigh Valley's 5-4 win over Rochester.
Burr was removed from Thursday's appearance versus the Rays with tightness in the back of his right shoulder, Corey Seidman of NBC Sports Philadelphia reports.
Burr signed a minor-league contract with the Phillies on Dec. 12.
Burr was placed on unconditional release waivers by the White Sox on Monday.
Burr was optioned to Triple-A Charlotte on Friday, LaMond Pope of the Chicago Tribune reports.
Burr (shoulder) was reinstated from the 10-day injured list Friday.
Burr was recalled from Triple-A Charlotte on Friday.
Burr was optioned to Triple-A Charlotte on Tuesday.
The White Sox recalled Burr from Triple-A Charlotte on Monday.
Burr (2-0) allowed two runs on three hits while striking out one but got the win over the Twins on Tuesday.