Peavy was hoping to throw between 80-100 pitches in what was viewed as his last rehab start before joining the White Sox, but he threw just 68 pitches.
The Chicago Tribune reported that Peavy had tightness near his throwing elbow.
Norfolk touched Peavy for two runs -- both earned -- on four hits. Peavy struck out four and walked one while throwing 43 of his pitches for strikes.
Peavy threw 80 pitches in his previous start on Monday, but he was hit in his throwing elbow, delaying his major-league debut for the Sox.