Bexley Council said its Environmental Health Teams are treating the matter as a priority.
Signs have been put up around the site warning people not to enter the lake or allow pets into the water.
Fishing has been prohibited and staff are patrolling the area regularly to ensure the restrictions are followed.
Blue-green algae, also known as cyanobacteria, are microscopic organisms naturally present in lakes and streams.
In warm, shallow, undisturbed, nutrient-rich waters that receive a lot of sunlight, they can multiply rapidly.
This can result in blooms that change the colour of the water or form mats or scums on the surface.
Some blue-green algae can produce toxins while others do not.
It is not possible to tell if a bloom is toxic by sight alone.
Exposure to high levels of blue-green algae blooms, whether through contact with the water, swallowing the water or inhaling airborne droplets, can cause illness in people and animals.
Symptoms in people can include diarrhoea, nausea, vomiting, skin, eye or throat irritation, allergic reactions and breathing difficulties.
The biggest risk is to pets, livestock and wildlife, which can become seriously ill or die if they come into contact with the toxins.
Bexley Council said more information will be released once further tests have been carried out.
A spokesperson for Bexley Council said: “Danson Lake is closed today and all activities on the lake have been suspended.
“Suspected blue-green algae has been found in the lake. Environmental Health Teams are looking into this as a matter of urgency.
“Blue-green algae can cause illness to humans and animals if they come into contact with it or it is swallowed.
“No fishing is allowed. Signs have been put up asking people not to enter the lake or allow pets to enter. Staff are regularly patrolling the lake
“We will be sharing more information shortly.”
