The clip, shot last Wednesday, shows the calf repeatedly popping its head out of the water so it can be petted by the group leaning over the edge of a boat.Dave Anderson from Captain Dave's Dolphin Safari, who posted the clip online this week, said it wasn't clear why the young whales liked having their gums rubbed but it was an amazing encounter for those on board.
"It was like God put a spotlight on that whale and said, 'Go and bless those people way beyond their wildest dreams!'" Mr Anderson told ninemsn.
"I do whale watching for a living and this was over the top, one of the best encounters with a whale I have ever seen."
In a comment posted with the video, Mr Anderson said the gray whale calf was from a pod off the Mexican state of Baja California."According to the naturalists who see them every day, these gray whale calves enjoy having people touch them, even in their mouth and on their baleen," he said.
"Even though these whales don't have teeth, perhaps it is like a teething child who enjoys having his gums rubbed."
He said no one fed the whale pod or did anything to encourage their visits.
"Gray whale moms will actually bring their baby over to be touched," he said.
"It only happens in Baja.
"This is how gray whales have become known as 'the friendliest whale'."
Gray whales migrate from Alaskan waters to the warmer Mexican coast to breed every year.
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