The three-month-old cub has been named Artico, Spanish for Arctic.
"His parents are normal Bengal tigers, orange with black stripes, but because of a genetic mutation he is completely white with no stripes," said Serafin Domenech, director of El Arca (The Ark) refuge in the south-eastern province of Alicante.
Artico's carers delayed announcing his birth until now because he was so weak when he was born they were not sure he would survive. The cub still has trouble digesting food and requires special care.
Domenech said such tigers are sometimes born in the wild but it is almost impossible for them to survive for long as their strange colouring causes them to be rejected or even attacked by other tigers.