It's a late 19th century idea that has no basis in the historical record. Poor Jews were not in the habit of packing up and going from Israel to India. The most explicit link between Jesus and India comes from Louis Jacolliot's La Bible dans l'Inde: Vie de Iezeus Christna in 1869 (though others had believed Jesus to have drawn on Eastern wisdom more generally - Voltaire is a representative of this argument). He did not argue that Jesus had traveled to India, but rather that the Jesus stories are Jewish retellings of Indian stories. This is part of a 19th century trend known as "Orientalism" (cf. Edward Said's book simply titled, Orientalism). There was a fetishization of the East and it (the East) was thought to have massive explanatory power for any number of ancient beliefs. Jacolliot, for instance, believed that similarities between Jesus and Hindu figures explained the Jesus story in toto. The belief that Jesus learned His wisdom in India rather than from Jews also had a pretty nasty history in early 20th century Germany, where Christ's Jewishness was denied and he was thought rather to have been Aryan (you can see this Eastern Jesus qua Aryan in Nietzsche's Thus Spake Zarathustra).