Thobela said Ambunda, whom he manages with Nestor Tobias, sustained a hamstring injury during training for the title fight that was to take place at the Manchester Arena in the UK on September 13.
"This is very sad," said Thobela yesterday.
"We put in a lot of effort and invested so much in this fight.
"We asked for a three-week postponement but promoter Eddie Hearn has not responded to our request."
Tobias, who also doubles up as the former WBO bantamweight champion's trainer, described the latest development as a huge setback.
"We were a few days away from another world title and this injury is a major blow, but unfortunately we don't have control over these things," Tobias said.
"We informed Quigg's camp in the United Kingdom and we know they will be very disappointed because this is a fight that the world was waiting to see."
Ambunda - whose first fight in the super bantamweight division was on May 17, when he won the WBA and IBF international belts on points over 12 rounds against Cristian Palma in Namibia - said he was disappointed.
"Obviously, I was looking forward to this fight to claim my second world title, but God works in mysterious ways," said the 34-year-old Namibian who lost the WBO bantamweight belt to highly respected Tomoki Kameda in the Philippines on August 1 last year.