The pair were due to fight on May 21 at the home of Derby County, Pride Park. Instead, Queensbury Promotions will have to find a new date for the event, with Andrade potentially needing surgery to fix his right shoulder issue.
In a statement, the organisers said: "Queensbury Promotions have been informed that Demetrius Andrade has sustained a shoulder injury, which has forced him to withdraw from his scheduled interim WBO world super-middleweight title fight with Zach Parker at Pride Park, Derby, on May 21.
"It is with great regret that the decision has been made to postpone the event until the extent of the injury is fully established. A further update will be released in the coming days with a revised fight date and information for ticket buyers."
Andrade, who is yet to taste defeat as a professional, recently defeated Jason Quigley to defend his WBO middleweight title for a fifth successive time and improve his record to 31-0 (19 wins by knockout).
The 34-year-old American has fought outside the United States once - beating Jack Culcay on a split decision in Ludwigshafen, Germany.
Parker is also undefeated and boasts a record of 22-0 (16 wins by knockout). His latest outing saw him dispatch Marcus Morrison in the fourth round at the Utilita Arena in Birmingham.
The 27-year-old is a big Derby County fan and was looking forward to living out his dream of fighting for a world title at Pride Park.
Queensbury Promotions were also looking to donate £10 from every ticket to support the football club, which has recently been relegated to League One.
Details on the rescheduled bout are due to be released by the organisers in the near future.