One officer can be heard saying “my god” as the discovery is made.
About 6,000 chicks from the original batch of 26,000 died when they were dumped at Barajas airport, said police who reported the discovery on Friday.
Of the remaining 20,000, just 3,200 were found still alive because of the appalling conditions they had been left in, police said.
The cargo of live chicks had arrived at the airport but no-one had claimed them and they were left in cardboard boxes for three days until they were discovered last Sunday.
Police said after heavy rain in Madrid, the boxes had broken which meant it was impossible to transport the birds to their intended destination in Spain.
The chicks were abandoned without anything for them to eat or drink in the cold until they were found.
Some of the survivors had eaten the remains of the birds which died.
The smell of the dead birds made the conditions even worse for the surviving chicks.
Spanish police have contacted the company which sent the chickens and which was responsible for their transport to their final destination.
Officers have been in touch with animal rescue associations to try to save the surviving chicks.
A National Police spokesman said: “We have launched an investigation into what happened with a view to taking action for a possible act of animal cruelty.”
Carolina Corral, of ALBA, an animal rights association, went to the airport an hour after receiving a photograph sent by police.
“It was enough to make my hair stand on end,” she told El Pais newspaper.
She said it was the worst example of animal cruelty she had witnessed.
“I was shocked. We did not have the experience to carry so many chicks nor the adequate infrastructure,” she added.
Ms Corral said she would give evidence in any prosecution.
Fernando Sánchez, president of the Salvando Peludos, an animal rescue association, also went to the airport and said the situation was “terrible”.
“We had not taken even a quarter of the chickens and many kept showing up,” he said.
Mr Sánchez said his organisation posted messages on social media to find homes for the 3,200 surviving chicks.
“We don't want them going to industrial farms but into people's homes. Already many vets and other people have taken one of the chickens,” he said.