The Advisory Council on the Misuse of Drugs (ACMD) said it would recommend UK Home Secretary Theresa May put the product marketed as "herbal incense" on the list of controlled substances.
The call comes after two girls, aged 11 and 12, were rushed to hospital after taking a legal high in Glasgow's Kelvingrove Park. They were treated at the city's Western Infirmary.
A 16-year-old girl has been detained in connection with the incident.
Annihilation can cause unconsciousness, increased heart rate, paranoia and self-harming and is believed to be being used predominantly by young people in Glasgow.
Police issued warnings on its use last week, after nine people were hospitalised.
ACMD chairman Professor Les Iversen told a meeting that the public body is "ahead of the game" with regards to the substance made from a synthetic form of cannabis.
He said: "Annihilation is a relatively new substance and product and the evidence for its prevalence and harms is still very preliminary.
"However, there have been reports, particularly from Glasgow, of young people reacting very unfavourably to this product, becoming severely agitated."
Prof Iversen described Annihilation as "particularly potent" and said its arrival showed just how fast-moving the legal high market had become in recent years.
However, Edinburgh drugs charity Crew said the problem with legal highs is that when one is made illegal, another one soon replaces it.
Katie MacLeod, outreach co-ordinator for the charity who specialises in legal highs, said: "With legal highs you don't know what's in them. They can have different active ingredients and it's difficult for users to know how much to take.
"Young or vulnerable users are very much at risk."
She added that making a substance illegal and the increased media coverage it attracts can often lead to a surge in people using the substance, as was the case when mephedrone – or meow meow – was banned last year.
On Saturday, Strathclyde Police issued a warning about Annihilation, saying it is one of many psychoactive substances that authorities have been made aware of in recent months.
Detective Inspector Jim Bradley, from Glasgow city centre police office, said: "Just because it's legal doesn't mean it's safe. No one can predict the risks. The symptoms appear, in some cases, to last for hours.
"Users can never be sure what they are taking or what the serious consequences can be."
Officers also warned users against mixing any legal high with other drugs or alcohol as the consequences could be even more severe.
Before making regulations related to drugs, the Home Secretary is obliged by law to consult the ACMD, a non- departmental public body which advises ministers on how to deal with the misuse of drugs.
