Jublee Tamuli had travelled 70km (43 miles) from her home for the exam in Assam's Tezpur town with her father, reports in the local press said.
Her father rushed to a market to buy a pair of trousers, but she said she took the curtain since the test was timed.
She later described it as the "most humiliating experience of my life".
"Is it a crime to wear shorts?" she asked reporters outside the exam centre. "All the girls wear shorts. And if they didn't want us to wear shorts, they should have mentioned it in the exam documents."
