Balfour Beatty was due to begin developing the structure over the A63 at Princes Quay later this year.
It is understood problems were discovered during early ground investigation works.
As a result the bridge, which was due to be completed by Easter 2017, would not have been completed until the end of 2017.
Hull City Council said "there was no alternative" but to delay the project as it would have caused "unacceptable disruption" throughout its City of Culture celebrations.
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The structure is being delivered as an early phase of a major project by Highways England (HE) to upgrade the A63.
Cllr Martin Mancey, Portfolio Holder for Energy City, said: "Of course, we are extremely disappointed by this news from HE but we are working hard to support and assist them and they have been clear that they remain committed to the development of the footbridge, which we are hopeful will start in 2018.
"If construction had gone ahead, the level of disruption it would have caused on the main arterial route in the city during our year as City of Culture would not have been acceptable.
"We are currently in discussions with HE to develop a detailed plan to improve the existing crossings across Castle Street in time for 2017, the details of which will be released shortly."
(LM)
