BERLIN—Within hours of her birth, 47 minutes into 2018, little Asel had attracted the attention of her home city, Vienna, as the capital’s “New Year’s Baby.”

But instead of good wishes from the citizens who read her birth announcement, the infant and her family were greeted with a wave of racism, disgust and hate.

Internet rights and refugee support groups say they had never seen a wave of hate directed at an infant to compare with the one that met Asel and her parents.

“In the first hours of her life, this sweet girl was already the target of an unbelievable wave of violent, hateful online commentary,” Klaus Schwertner, secretary-general of the Vienna chapter of the Roman Catholic charity Caritas, wrote on his Facebook page.

“It is a completely new dimension of online hate, targeting an innocent newborn,” he said.

Many of the comments that filled the social media pages of Austrian media outlets that carried the picture of Asel’s family also targeted the baby’s mother, whose smiling face was encircled by a head scarf.

“I’m hoping for a crib death,” wrote one user. “Deport the scum immediately,” read another posting to Heute’s Facebook page.

Not all the comments were negative, and some users drew a parallel between the online uproar over the image of the young Muslim and the entry of the far-right Freedom Party into the country’s new right-leaning government, sworn in weeks before her birth.

Schwertner sought to turn the sentiment around, calling on his followers to stand up for the young family in an outpouring of social media support. By Thursday, more than 10,000 people had shared his message and more than 17,000 people posted hearts, along with words of congratulations, support and encouragement.