In a video of the incident, a man can be seen placing the toddler wrapped in banana leaves on a charcoal bed in Allapur in Dharwad district during Muharram observance.
The video showed the baby crying and struggling to escape the heat as smoke kept emanating from the charcoal.
"The parents of the baby had prayed for a boy two years ago. On their wish being fulfilled, they had come to fulfil their promise. The baby was placed on a bed of charcoal that was doused off. As it was slightly hot, banana leaves were used. It was for just couple of seconds," police said.
The police said no case has been registered in connection with the bizarre ritual, but added the Child Welfare Committee has been informed with a request to counsel the parents.
The incident has come to light only a few days after the Karnataka cabinet cleared its much-awaited legislation to end "inhuman evil practices", popularly known as the anti- superstition bill.
The proposed 'Karnataka Prevention and Eradication of Inhuman Evil Practices and Black Magic Bill, 2017' - to be tabled in the next assembly session - seeks to prohibit coercing any person or persons to perform fire walk.