An official said the tigers pounced on him because one of the four enclosure gates was not properly latched.
White tigers derive their colour from a recessive gene.
The keeper had only been employed by the national park for a little over a week.
His angry relatives protested outside the park on Sunday - they want financial compensation from park management, accusing them of negligence.
A keeper at the park near Bangalore was reported to have been injured two years ago by lions.
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