Barrow Borough Council's licensing committee spent three days considering David Gill's request.
But the council refused permission for the extension after inspectors raised concerns about "out-of-date practices".
Karen Brewer, the zoo's chief executive officer, said great strides had been made to improve the zoo and keep it the "unique attraction" it is.
Whoever takes over running the zoo must apply for a new licence within the next six months.
Mr Gill first received a licence to run the zoo in May 1994, when the attraction consisted of 290 animals on 12 acres with about 200 visitors a day.
Now the zoo is home to more than 1,000 animals across 50 acres, attracting more than 250,000 visitors and generating Â£3m a year.
The council has gone along with an inspector's recommendation that the licence, which must be renewed every six years, should not be reissued until new management is in place at the zoo.
A report to the committee said: "Of particular concern to the inspectors is the fact that as this zoo grows, it relies heavily on (Mr Gill's) experience implementing out-of-date practices and refusing to implement modern zoo practices.
"This has resulted in animal welfare issues, a higher than expected mortality rate amongst the animals, higher than expected incidents (such as injuries to the public from animals), and places both staff and the public potentially in danger."
The council said Mr Gill had installed new management but there were concerns about him, as licence holder, overruling other management decisions.
Ms Brewer said: "I am confident in my own position to manage the zoo without David here on a regular basis but we do need his ideas and his contribution in this zoo as it is vital to keep its heart alive."
Councillors have refused to renew the licence of the owner and founder of South Lakes Safari Zoo.