Animal rights activists and others have branded Francisco Rivera Ordonez "irresponsible" and "an idiot".
But fellow bullfighters have tweeted their support and shown pictures of other children around the animals.
A caption accompanying the photograph, which was uploaded to Instagram on Monday, refers to the episode as the five month old`s "debut".
Mr Rivera has responded to the row by saying: "She is never going to be safer than she is in my arms."
However, the Andalusian authorities said they "totally rejected" his actions and had referred the case to prosecutors.
"We hope that such behaviour is not repeated and that the social media reaction ensures that it is not accepted as normal," the ombudsman`s office said in a statement (in Spanish).
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