"We know that mortality among cubs is very high in the first weeks, but we are still depressed and it's making us sad," said Florian Sicks, polar bear keeper at the Tierpark in the east of the city.
Eight-year-old mother Tonja had taken "exemplary" care of her baby, which was still healthy and nursing on New Year's Day, the zoo said in its statement.
But the cub - which had not yet been given a name - appeared lifeless when staff checked a surveillance camera in the bears' enclosure on Tuesday morning.
Scientists at Berlin's Leibniz Institute for Zoo and Wildlife Research (IZW) will carry out an autopsy on the baby bear to determine the cause of death.
Tuesday's news was the second polar bear cub death within a year for the Tierpark, which lost four-month-old Fritz to hepatitis in March last year.
Berliners had reacted enthusiastically to the arrival of Fritz, the first cub born in the former East Berlin zoo in 22 years.
Many hoped he would take the place in Germans' hearts once occupied by Knut, the universally adored polar bear born in 2006 and raised by west Berlin zookeepers after being rejected by his mother.
Knut's worldwide fame brought in millions of euros from visits and merchandising before his untimely death in 2011.