The message on social media yesterday advising people to prepare for an emergency evacuation sparked an online backlash.
They advised residents to prepare an emergency bag "in case you need to flee your home immediately".
The image of a rucksack advised it should contain amongst other things, seasonal clothing, food and water, a first aid kit, batteries, a whistle and a torch.
Hundreds of social media users demanded an explanation for the post.
"We're sorry to have caused alarm," the council said. The post was part of a national "Preparedness Month" campaign.
Tooting MP, Dr Rosena Allin-Khan said
"without any context" the tweet suggested "a zombie apocalypse
is imminent".
The council is taking
part in #30days30waysUK, which aims "to build household and community
preparedness and resilience".