More than 11,000 signatures have been gathered in the online petition and a Facebook page attacking the new feature has been launched.
Critics accuse officials of opting for the installation for fear of offending non-Christians, especially Muslims.
But the mayor’s office said it was part of a theme this year of “light”.
Traditionally, a 20 m (65 ft) pine tree taken from the forests of the Ardennes has adorned the city’s central square, the Grand Place.
This year, it has been replaced with a 25 m (82 ft) construction, though smaller real Christmas trees still decorate the square, a spokesman at the mayor’s office said.
The city’s website said the new “tree” was one of five “light” installations around the Grand Place this year, offering visitors the chance to climb to the top and enjoy “beautiful views” of the city.
Tourism councilor Philippe Close at the mayor’s office said the aim was to show off the “avant-garde character” of Brussels by blending the modern and the traditional, to produce something new and different.
Brussels hosts one of the most popular winter markets in Europe and many are worried that the contemporary construction is incongruous with the 17th-Century buildings that surround it.
The light installation has even been nicknamed The Pharmacy by some who say the glowing cubes resemble the green cross symbol you find outside many chemists around the world.
Bianca Debaets, a Brussels councilor from the Christian Democratic and Flemish party, said she believed a “misplaced argument” over religious sensitivities had moved Brussels to put up the light sculpture.
“For a lot of people who are not Christians, the tree there is offensive to them,” she told reporters.
Erik Maxwell, from Brussels, said: “We think the tree has been put up for cultural reasons.
“A tree is for Christmas and Christians but now there are a lot of Muslims here in Brussels. So to avoid discussions they have just replaced a tree with a couple of cubes! I am more traditional, I prefer the usual tree. That’s better for the Belgian people.”
A recent estimate in the Belgian newspaper Le Soir suggested Muslims made up 22% of the population of Brussels and its region as of 2010.
Parts of the Belgian press have been keen to suggest that the tree is an example of “political correctness”, designed to be more appealing to non-Christian religious groups than a traditional fir tree.
However, it seems likely that the media storm is influencing public opinion rather than reflecting it.
There was applause and plenty of “oohs” and “aahs” in the square at a preview of the nightly sound-and-light show that will take place there until the New Year.
“What we want is just to modernise the pleasure of winter, of this Christmas market and all the image of Brussels,” said Councillor Philippe Close.
“The Christmas tree is not a religious symbol and actually lots of Muslims have a Christmas tree at home.
“For people who want a traditional religious symbol, we have the nativity scene here in the square. For people who want modernity, we have this new tree.”
Semsettin Ugurlu, chairman of the Belgian Muslim Executive, representing the Muslim community in Belgium, said his organization did not mind any kind of Christmas tree.
“We know we are living in a country with a Christian culture, we take no offence over a traditional Christmas tree,” he said.
Miryam Oostling, a visitor from Leeuwarden in the Netherlands, said: “I quite like the tree. It’s a piece of modern art. It’s cosy!”
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