The Department of Energy and Climate Change is spending £6m on the ad, which was created by AMV BBDO, to promote its Act on CO2 carbon reduction initiative.
The ad is designed to make adults feel guilty about the legacy they will leave their children and features a father telling his daughter a bedtime story of "a very very strange" world with "horrible consequences" for today's children.
It shows a British town deep under water, with people and animals drowning. Carbon dioxide is shown rising from cars, homes and everyday appliances in clouds of black soot, which then form a jagged-toothed monster.
The launch of the activity marks the first time that a government ad campaign conveys the message in a factual way that the human race is causing global warming and endangering life on Earth.
According to an ASA spokesman, 357 people have complained since the ad launched on 9 October.
The complaints include objections about the existence of climate change, objections to the ad's claim that climate change is man-made, and questions as to whether there is a scientific consensus about it.
In relation to the second point, the ad includes the line: "The grown-ups discovered that over 40% of the CO2 comes from everyday things like keeping houses warm and driving cars".
While most complaints claim the ad is misleading, some have also said it is frightening for children.
The DECC launched the campaign after government research revealed that more than half the population think that climate change will have no effect on them.
Joan Ruddock, the energy and climate change minister, defended the campaign last week, saying: "The Department of Energy and Climate Change stands by the messages in the television ad, and the creative approach.
"The ad is directed at adults, but we know that the proposition to 'protect the next generation' is a motivating one.
"Climate change is not just a problem for generations of people far in the future, it is happening now, it affects us and our children, and we owe it to them to take action now to prevent its worst effects."