The American-born defender looked set for a move to the Liberty Stadium after a deal between the two clubs was agreed.
But the 25-year-old has since undergone a hip operation, so Whitbread will stay with the League One club for the time being.
"We agreed a deal for Zak with Millwall, but because he has just had a hip operation, the player felt it was better if he remained at the club until he was fully fit again." Swansea chairman Huw Jenkins told the club's official website.
"We will review the situation again in January."