In a 23-page letter dated 7 October but only published today, the European Commission pointed out that it "has doubts.... as to [the deal's] compatibility with the internal market"
It added that it "takes the view, at this stage, that it constitutes state aid".
The Luxembourgish authorities confer an advantage on Amazon.... [the] advantage is obtained every year and [is] ongoing.... [and] is also granted in a selective manner.
For its part, Amazon pointed out that it had been entirely open about the affair, saying it was subject to exactly the same laws as all other companies operating in the country.
But this is part of a wider crackdown by European authorities on states using low tax rates to lure companies. In recent times, Swiss banks have been ordered to hand over details of their customers, while companies such as Apple and Starbucks, which routed their tax affairs through Ireland to take advantage of the "double Irish" tax loophole, have found themselves under heavy scrutiny.
However, Luxembourg has found itself at the centre of criticism after leaked documents - known fondly as "LuxLeaks" - showed in detail how it had helped companies to channel profits through the country in order to pay low tax rates.
New European Commission president Jean-Claude Juncker, the country's former prime minister, has also come in for criticism over the role he played.