May was cut loose by Chicago on Saturday, Paul Sullivan of the Chicago Tribune reports.
May has been optioned to Triple-A Charlotte, Daryl Van Schouwen of the Chicago Sun-Times reports.
May entered Saturday's game as a pinch hitter and delivered his first hit in the major leagues. He went 1-for-2 with a strikeout in a 7-0 loss to Cleveland.
May returned to the lineup Saturday after sitting three straight games. He went 0-for-3 with two strikeouts in the White Sox's 6-0 loss to the Twins.
May is not in the lineup Thursday against the Indians.
May is not in the lineup Wednesday against the Twins.
May is out of the starting lineup for Friday's series opener against the Twins.
May went 0-for-4 with two strikeouts and an RBI groundout in Tuesday's 6-3 loss to the Tigers.
May started in center field and batted ninth in the order in Friday's exhibition against the Brewers.
May, who had two hits as the leadoff hitter Tuesday, will not bat leadoff immediately for the White Sox, Colleen Kane of the Chicago Tribune reports. Manager Rick Renteria said May might eventually be a leadoff hitter.