The male lions, Majo and Motshegetsi, broke out of their enclosure and leapt over a moat at 08:40 (06:40 GMT) on Thursday, before the zoo opened.
They were discovered in undergrowth in a terrified state.
Although one of the lions was ushered back to its enclosure, the other remained agitated and had to be shot.
"This is a very, very sad ending, which I really would not have wished for," zoo director Joerg Junhold told reporters. "But in this case personal safety had to take priority."
How zoos prepare for an escape
The two animals, known as Etosha lions after an area of Namibia, arrived at Leipzig zoo only last month from the Swiss city of Basel.
After the lions were found only a short distance from their enclosure, around 40 zookeepers surrounded them with vehicles in an attempt to usher them back.
They succeeded in returning one of the animals three hours later with the aid of a fence, but the other lion became agitated as they tried to tranquillise it.
Local media said Majo had survived, but Motshegetsi had been killed.
The enclosure had been at the zoo for 15 years, the director said. They had never had problems before but would now review security.
Crowds built up at the entrance to the zoo, but it was largely was closed on Thursday because of the lions' escape.
The last time lions escaped from their enclosure in Leipzig zoo was in 1913, prompting a widespread hunt that ended with all six lions being killed, the Leipziger Volkszeitung reported.
One of two lions that escaped from an enclosure in Leipzig zoo in Germany has been shot dead after attempts to use a tranquilliser failed.