Rodriguez, who earned the wrath of General Manager Brian Cashman last week by tweeting he had been cleared by doctors to begin playing after undergoing hip surgery, will join Class A Charleston, S.C., Tuesday.
He is expected to play at least three innings at third base in the minor league squad's game against Rome, N.Y.
The 37-year-old has yet to make appearance for New York this season following January surgery to repair a torn labrum in his left hip.
The Yankees, mired in a five-game losing streak and 6 1/2 games behind Boston in the American League East, could see the return of the controversial slugger before the All-Star Game break if the rehab assignment goes well.
New York has suffered from poor production from his replacements at third base, who have combined to hit just .231 with four homers and 23 RBI.
"A-Rod" returns while under suspicion of using performance-enhancing drugs as part of the investigation of Biogenesis of America, a Miami-based anti-aging clinic accused of supplying PEDs to an array of major league players.