The zoo said the cub, which hadn't been named, appeared healthy yesterday but zookeepers found it dead when they checked a surveillance camera today.
It said that an autopsy is being carried out on the cub, which was 26 days old.
Tonja's first cub, Fritz, died of unknown causes in March at the age of four months.
The mortality rate for young polar bears is about 50 per cent and can be even higher during the first 10 days.
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