The chef’s petition, which received over 144,000 signatures, called for a tax of 7p per regular sized can.
The Department of Health (DH) said in a statement: "The Government has no plans to introduce a tax on sugar-sweetened beverages.
“The Government has committed to a tax lock to avoid raising the cost of living and to promote UK productivity and economic growth, however, the Government keeps all taxes under review, with decisions being a matter for the Chancellor as part of the Budget process."
The DH added that reducing obesity required a ‘comprehensive and broad approach’ and that further plans to tackle the issue would be announced by the end of the year.
Campaign group Sustain – who launched the petition with Oliver – called the decision 'absurd'.
"If the government is serious about tackling childhood obesity and diet-related ill health, then a sugary drinks duty must be one of the options that is on the table for consideration," said Malcolm Clark, coordinator of Sustain's Children’s Food Campaign.
“There is real public appetite for robust measures that will make a difference, rather than a rehash of the failed Responsibility Deal, which has not.”
While Oliver is yet to publicly comment on the decision, he retweeted a link to a response from the British Dental Health Foundation which said the Government was ‘deeply irresponsible’ and had ‘let down millions of people’.
"We absolutely believe the government have failed to listen to the public majority in the calls for a ‘sugar tax',” said Dr Nigel Carter OBE, chief executive of the British Dental Health Foundation.
"The government response was centred on obesity but worryingly completely omitted other crucial health issues such as diabetes and dental health.”
Children’s tooth extractions cost the NHS around £30m per year, with 26,000 primary school age children admitted to hospital with tooth decay in the last year.
"What is happening right now in dental surgeries and hospitals across the country cannot be allowed to continue,” said Carter.
“The introduction of a ‘sugar tax' would go a long way to changing the way we all view sugar.”
Oliver made headlines earlier this year when he imposed a 10p tax on sugary drinks at his Jamie's UK restaurants - including the 41-strong Jamie's Italian brand.
He is urging other restaurant groups to follow suit, though so far only Leon, Abokado and Angela Reed Café & Bakery have voluntarily signed up.