One penguin is dead and two others are missing at the Dortmund Zoo as police in Germany said they are investigating a possible string of crimes.

One Humboldt penguin was found dead in the zoo's flamingo cage on Monday morning and two others are missing, police spokesman Marco Mueller said.

He said police are trying to determine if someone stole the birds or if they had somehow escaped.

"The loss breaks our hearts," zoo director Frank Brandstaetter told reporters in Dortmund, saying the one-year-old birds had been born and raised at the zoo.

In November, a 21-year-old sea lion named Holly was found dead in her enclosure at the zoo with a smashed skull and three teeth missing. And in August, three pygmy marmosets and two acouchi rodents vanished.

Mueller says police have not yet determined if the incidents are linked.

"That's part of our investigation," he said.

The zoo is adding more security personnel and watch dogs, Mr Brandstaetter said.