Rodriguez signed a contract with the Wei Chuan Dragons of the Chinese Professional Baseball League on Wednesday.
Rodriguez elected free agency Monday.
The Brewers outrighted Rodriguez to their alternate training site Wednesday, Todd Rosiak of the Milwaukee Journal Sentinel reports.
The Brewers designated Rodriguez for assignment Monday.
Rodriguez was optioned to Triple-A San Antonio on Wednesday.
Rodriguez went 2-for-3 with two RBI in Tuesday's spring game against the Royals.
Rodriguez was claimed off waivers by the Brewers on Monday.
Rodriguez went 2-for-4 with a solo home run in Sunday's 5-3 loss to the White Sox.
Rodriguez is starting at third base and batting fifth in Sunday's game against the White Sox.
Rodriguez remains on the bench Sunday against the Orioles, Roch Kubatko of MASN Sports reports.