"The Blade" is the first in a series of temporary art pieces marking Hull's year as UK City of Culture.
It was placed in Queen Victoria Square after being transported from the new Siemens turbine factory in east Hull.
The Hull Daily Mail reports that Hull 2017 organisers are now preparing a planning application.
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Hull City Council planning manager, Alex Codd, said: "Nationally, planning permission is not needed on a piece of land that is being used for an event that is to last up to 28 days.
"However, as the installation will be temporarily located in Queen Victoria Square for longer [than] this, we understand the Hull 2017 team are now preparing an application for planning permission, which will then go through our usual planning process."
City of Culture chief executive Martin Green said: "We worked closely with the council and because the artist wanted it to be a surprise we agreed that planning permission would go in after the installation.
"Thousands of people have visited Blade and it has achieved national and international headlines.
"This is a great example of Hull City Council and the Culture Company working together."
A 250ft-long (75m) wind turbine installed as a piece of artwork in Hull does not have planning permission, the city council has confirmed.