One of the divers was 32-year-old marine biologist Gigi Torras.
Torras said last Friday that the rescue was a great birthday present for her - the 'best ever' in her words. She also felt that she received a little gesture of appreciation from the giant mammal itself.
"It was like out of this world, it was incredible, just incredible," she told Reuters on Tuesday. It was only the third time that a humpback has been seen around the Balearic Islands.
How did they rescue the whale?
They discovered the whale completely trapped in the red fishnet so it could not even open its mouth.
After initial attempts to cut the net from a boat failed, divers from Albatros and Skualo diving centres joined the effort and plunged into the sea to remove the mesh with their knives in a daring 45-minute operation.
"The first ten seconds she got a bit nervous, you know, like bubbles everywhere, but then I don't know, call me crazy but I think she knew we were there to help her and she just relaxed and we started working from the front of her mouth backwards," said Albatros owner Torras.
"We kept cutting and cutting and she kind of gave a little wiggle to get herself out of it," Torras said, adding that the mammal then stayed for a bit to regain her strength in the company of the four divers and even gave what looked like "a little thank you sign" before swimming off.
Nicknamed "walls of death" for the quantity of other sea life they catch in addition to the fish they are set for, drift nets were banned by the United Nations 30 years ago.
Watch the video above to see the rescue in action.