Passengers will be met with demonstration on the quay, that is organised by a couple of environmental groups against more cruise ship arrivals.
They claim that the big vessels create pollution and overcrowding of the "already saturated islands," and staff onboard are being "exploited."
The mega cruise ship, weighing 228,000 GT and capable of carrying a total of 6,680 passengers, is sailing the world as part of its debut cruise.
An official welcome is due in Palma, but police may have to be called in as the protest groups have put out rallying call for more people to join.
The Balearic Group of Ornithology and Defense of Nature (GOB) said Symphony of the Seas represented everything it disliked, "pollution, mass tourism and labour exploitation."