Jon Platt was taken to court after refusing to pay a Â£120 fine for taking his daughter, aged six, to Florida.
He had argued the law only required children to attend school regularly.
The council said it wanted to know why the court decided there was no case to answer.
Mr Platt, a solicitor, took his daughter on holiday with the extended family, despite an absence request being rejected by the school.
At a magistrates' court earlier this month he successfully argued Section 444 of the Education Act required parents ensured their children attended school "regularly", and did not put restrictions on taking them on holidays in term time.
His daughter had a 93.8% attendance rate the previous academic year.
Isle of Wight Council said it has started the formal process of appeal to the High Court for clarification on a matter of law.
Council leader Jonathan Bacon said: "The recent media attention given to this case shows that there is interest, concern and, above all, uncertainty as to what constitutes 'regular attendance' for the purposes of the legislation in question.
"The Isle of Wight Council has received clear advice that the magistrates may have failed to interpret and apply the law correctly in making their decision.
"Where the law created by Parliament is uncertain, the appeal courts have the ability to lay down a binding ruling as to the correct interpretation of the law."

It’s rare that the company delves too far into how the “magic” - as they call it - works. Their logic is a magic trick doesn’t get better if you know how it’s done.
On Saturday, Disney - quite uncharacteristically - gave us a bit of an insight into how they plan to use technology to bring their much-loved brand of storytelling to new forms, by using robotics and artificial intelligence.
Jon Snoddy, the company's senior Vice President for research and development, explained how soon you’ll be able to interact with story-telling robots at Disney parks.
“I think AI [artificial intelligence] and machine learning is going to be very important for what we do,” he told the BBC.
"Things like characters that can move around among our guests. They’re going to need to understand where they’re going, have goals, and they’re going to have to know how to navigate in a world with humans.
"All these emerging technologies are going to be key to the next generation of entertainment.”
Robotic Pascal
During a panel discussion, the company shared footage - which unfortunately we’re not able republish here - of a robotic Pascal, the cute lizard from 2010 movie Tangled.
It’s a terrific recreation of the digital character, but the real challenge for Disney will be to avoid the so-called “uncanny valley” - the theory that if something is very lifelike, but not exactly right, it can be slightly creepy or disturbing.
"Obviously we’re not the business of scaring kids!” Mr Snoddy said.
"That won’t be part of what we deploy. We go and do tests in our parks to gauge the reaction and try and understand what kids find entertaining about these things. Our ability to build these characters at a fidelity that looks like the films is really growing.”
When these technologies are fully deployed in Disney parks, and perhaps as toys, Mr Snoddy said Disney will do everything it can to hide the inner technological workings.
"Every new technology that’s come along for the last 60, 70 years we have adopted and co-opted and made it into a story telling medium,” he said.
"This won’t be different. We’re not going to put up a sign that says 'Look! Artificial intelligence', because no-one would come to see that. They really come to be moved emotionally, that will not change.”
Isle of Wight Council begins a High Court appeal after the case against a father who took his child on holiday during term-time was thrown out by magistrates.
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Ever since Steamboat Willie, the iconic animated clip from 1928 featuring a mouse that would later become Mickey, Disney has had a proud record of innovating with new technology.