Unlike the major currencies of the world like the dollar, the pound, the yen and the euro, the rupee does not have a globally recognised symbol.
The new symbol would be the "identity of the Indian currency," says a finance ministry official.
The contest, which closed on 15 April, is open only to resident Indians, a release on the ministry website says.
The rupee is generally shortened to Rs or sometimes the currency is described as INR (Indian rupee).
But, the government says, these are not symbols, they are mere abbreviations for rupee.
To get an internationally-accepted symbol, the finance ministry has invited entries from the public.
the INDIAn Rupee notes
"The symbol should represent the historical and cultural ethos of India," says the deputy secretary in the finance ministry's coin and currency department, BS Rawat,.
"The entries can be in any of the Indian languages. They can even be in English which is also an accepted language of use by the government," Mr Rawat said.
Each entry has to be accompanied by a fee of 500 rupees ($10) and a participant can send a maximum of two entries.
The rules also say that the "symbol should be applicable to the standard [computer] keyboard".
Officials say the winning entry will be chosen by a seven-member jury of experts drawn from various art institutes, the government and India's central bank, the Reserve Bank of India.
Five shortlisted entries for the final selection were to be awarded a prize of 25,000 rupees ($500) and the winner will take 250,000 rupees ($5,000).
"The final selected symbol were to become the property of the government and the designer will have no rights over it any more," Mr Rawat said.
Experts say implementing a new currency symbol can be an expensive exercise.
According to one estimate, when the euro was introduced in 1999 it cost Europe's biggest companies more than $50bn to update their computer systems to deal with the changeover.
"We have not thought about the costs yet," Mr Rawat said. "First, we'll select a symbol and then we'll do the costing," he added.
The contest closed on 15 April at 1300 local time (0730G).Detailed guidelines on how to prepare the entries have been put up on the Indian finance ministry's website.