Spain's new Socialist government on Monday said it would allow the boat to dock at its eastern port of Valencia after Italy and Malta refused to accept it.
The Aquarius, which is run by SOS Mediterranee and MSF, is expected to arrive in Valencia at the weekend.
"The detour of the Aquarius is clearly a symbol of the failure of the European Union and European governments with their contradictory policies," the head of MSF Spain, David Noguera, told AFP by telephone from Barcelona.
"It is a very negative precedent. The truth is there is a question on the table as to whether this is a single event which is resolved quickly, or if we will no longer be allowed to dock in Italy and the blockage continues which would completely change rescue operations."
The Aquarius rescued the migrants including 123 unaccompanied minors, 11 other children and several pregnant women, from inflatable boats and rafts off the coast of Libya and took them toward Italy, but the country's new far-right Interior Minister Matteo Salvini barred it from docking, saying it should go to Malta.
Malta also refused to take the ship, saying it was Italy's responsibility since the rescue was overseen by the Italian coastguard.
Salvini declared victory after the standoff over the fate of the hundred of migrants on board prompted Spain to agree to accept them.
"That the Aquarius was diverted to Spain is not a victory for anyone, not for Salvini although he thinks so, and not for MSF or the European Union and especially not for the refugees," Noguera said.
"Today a boat that should be rescuing people at sea will spend 10 days outside of the rescue zone, and that will cause more deaths, that is obvious."
The 629 migrants on board the Aquarius come from 26 different countries -- 23 in Africa in addition to Afghanistan, Bangladesh and Pakistan, according to MSF Spain.
Spain's new Prime Minister Pedro Sanchez, who toppled his conservative predecessor Mariano Rajoy in a no-confidence vote on June 1st after a corruption scandal, made his offer to accept the migrants after the left-wing mayors of Valencia and Barcelona both offered to take the boat in at their ports.
"We obviously thank the Spanish government for the gesture, but we ask that it not be a one-off gesture, that it lead the European Union in a change of policies, so that the response to this phenomena is more human," Noguera said.
By Laurence Boutreux