He was reacting to the statement of RSS chief Mohan Bhagwat that anybody living in India was a Hindu.
"The theory that one who is born in India is Hindu has no logic behind it since it will eliminate the basic structure of society," the Shankaracharya told reporters in Vrindavan.
A real Hindu has faith in the Vedas and Shastras, while Muslims read the Quran and Hadith and Christians follow the Bible, he said.
On the Ayodhya temple dispute, the Shankaracharya said that political parties did not have the right to build a Ram temple in Ayodhya. "Only Shankaracharyas and Dharmacharyas have the right to construct a temple in Ayodhya," he added.
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The government too cannot construct a temple as India is "a secular (dharm nirpeksh) country", he said.
On a controversy surrounding the use of electronic voting machines (EVMs) in elections, the Hindu religious leader said that he was in favour of the use of ballot papers.
He said that pollution in the Ganga and Yamuna rivers has increased manifold and added that the government should shut dams or barrages on the two rivers to allow them to carry their natural flows of water.