Weeks, who last year batted .303 with 26 doubles over 97 games, was sent to Class AAA Sacramento following Oakland's acquisition of Drew from the Diamondbacks.
The A's sent a minor leaguer to Arizona in exchange for the former first-round draft pick, who is hitting .193 over 40 games.
Weeks was considered a fixture in the future of the Athletics, who are in contention for an American League wild-card spot. But he could manage only a .220 average through 113 games this season.
"For some reason, I feel like I was prepared for this news," Weeks told the San Jose (Calif.) Mercury News.