His side, Poole, were hoping to have him available to make his debut in Wednesday’s tie against Coventry.
The American speedway icon was drafted in to replace injured world champion Chris Holder, but the Pirates nonetheless comfortably beat the Bees 56-38 to extend Coventry’s poor away form.
Poole owner Matt Ford has called on his team to put the blow of losing the 43-year-old to one side.
He said: "Naturally I am very disappointed that the appearance of Greg will be delayed for us due to circumstances beyond our control.
“But right now it is really important that we put that to the back of our minds.”
Poole reverted to their previous one-to-seven and operated rider replacement for Holder during the win, but hope Hancock will have his passport back in time to make his bow at home to Eastbourne on Monday.