It will be installed in an empty niche at the west front of the Minster to mark her Platinum Jubilee in 2022.
Although approved, the council wants to see the final design once it has been selected by the Queen.
The details of the sculpture are a closely guarded secret and will be revealed at a public event next year.</span>
It will be carved by York Minster's own stonemasons and has been described as a "symbol of hope" in the aftermath of the Covid pandemic.
The statue will overlook a new public square, proposed for Duncombe Place, to be called Queen Elizabeth Square, according to the Local Democracy Reporting Service.
A York Minster report on plans for the statue and square says they are part of a project that will "signal the recovery and resurgence of the city from the ravages of the Covid-19 pandemic and as a symbol of hope".
A planning notice said the sculpture "will facilitate some repair work to the existing west front of the Minster while also being an addition to the overall history and story of York Minster and its purpose".
It added: "The west front already contains figures of saints, powerful figures in the church and secular figures.
"The proposals to include a sculpture of the sovereign would continue this theme, as they are at the head of the Church of England."
The statue also needs approval under the Care of Cathedrals Measure Act, monument consent and approval from the Queen.