The islands are famous for their huge populations of the sea birds, but in the past they have been hit by mysterious ailments.
Now, thousands of the gentoo and Magellanic penguins have been found on beaches partially paralysed and dying.
The birds have failed to reach breeding grounds and naturalists have no definite explanation.
One possible cause is poisoning by a "red tide" caused by an explosion of a type of microscopic sea plant.
Researchers from Falklands Conservation have been sent to areas where birds have been found, and specialist vets are also studying the problem.
Toxin magnification
A Falklands Conservation spokesman said: "At present, the causes are still unknown.
"However, it seems that opinion is starting to favour a 'red tide' event, leading to poisoning of birds and top predators.
"Red tides are caused by dinoflagellates, a microscopic red phytoplankton which blooms under certain conditions to dangerous levels in the water.
"These tiny plants are fed on by larger animals which concentrate the toxins in their tissues.
"When eaten by a larger predator such as a penguin, large numbers of these animals can prove fatal.
"Recently, a red tide algal bloom has led to the closure of several shell fisheries along the Patagonian coast, from the Santa Cruz coast to Chubut."
Largest population
Researchers are taking samples from the sea to check for the presence of the toxic algae.
"We hope that this will either confirm or rule out a red tide as an option," the spokesman said.
The Falklands population of gentoo penguins was estimated last year at over 115,000 - the largest population in the world, representing over 40% of the total species.