The team also transferred left-handed pitcher Joe Thatcher from the 15-day to the 60-day DL.
Hudson was hurt Tuesday night in a 6-5 win against Pittsburgh. He was hitting .245 with six RBIs.
Forsythe hit .291 with four home runs and 15 RBIs in 22 games for Tucson. His first appearance will be his major league debut.
Thatcher, who began the season on the DL, underwent exploratory surgery on Monday on his strained left shoulder.