Asel Tamga became the first Austrian born in 2018. Her birth was celebrated in the local press with a photo of the happy family in which her mother wore a hijab.
A deluge of racist and hateful comments followed on social media, forcing President Alexander Van der Bellen, 73, to step in.
He shared a Facebook post condemning the hateful attacks on Baby Asel, and added his own stern words of wisdom.
After wishing Asel welcome to the world, he added that; 'all people are born free and equal to dignity and rights.
'Confidence and cohesion are greater than hatred and incitement.'
Naime and Alper Tamga from Vienna welcomed daughter Asel at 00.47 on New Year's Day, making her the first baby born in Austria in the new year, according to the Daily Mail.
A photo of the family was shared on Facebook and a rash of racist comments followed among the thousands of well wishes.
One social media user commented: 'The next terrorist is born.'
Another person wrote: 'Does the woman have cancer? Or why does she otherwise wear a headscarf?'
The abuse was so severe that Facebook ended up removing the post, local news reports.
Austrian NGO Netpeace said the deluge of hateful comments is proof that online hatred is growing out of control as social media users even manage to turn a happy family picture into hate speech about religion and ethnicity.
The NGO said it is remarkable that so many people are nowadays even posting such comments under their real name instead of using an alias.
Netpeace spokeswoman Sabine Beck said: 'We think that this present case shows that it is about time to take measures.
'We urge the Federal Government to take extensive measures. These range from media education in schools to reinforcement of public prosecutor's offices.'
The hateful messages come amid tensions in Austrian society over the migrant influx to Europe and Islam.
The country's new conservative Chancellor Sebastian Kurz's coalition includes a far-right party.
One of the hostile messages to the baby's family referred to the new far-right interior minister Herbert Kickl, saying he 'is going to send you out of the country. He's the man to do it.'