Singh, accompanied by his wife Gursharan Kaur, ended a two-day tour of the 390 square-kilometre (150 square-mile) Ranthambore game park by seeing a tiger from a few feet away on a trip planned to drum up support to save the endangered animal.
Singh, 72, sighted the full-grown tigress from a distance of five feetmetres) 20 minutes into his drive through the park in the northern desert state of Rajasthan.
"I was lucky to spot a tigress called Lady of the Lake," Singh told reporters in a televised press conference.
Singh made the visit to Ranthambore to highlight a national trend of poaching and shrinking habitat that threatens the endangered species, with more than half the park's 35 tigers believed to have been killed since 2001.
Last week, the government admitted in court that poachers had killed 122 of the endangered big cats in India between 1999 and 2003, despite a national conservation programme.
Between 3,500 and 3,700 Indian tigers are left in the wild in India, according to official government estimates, down from about 40,000 tigers before India's 1947 independence from Britain.
"We have to recognise that our diversity, the whole bio-diversity system is under pressure as population increases," Singh told reporters after his tour of the park.
"This is the challenge we have to address. We have a problem at hand and if we don't tackle it, we would be doing an irretrievable damage to ourselves."
Tiger hunting is illegal worldwide and the trade in tiger skins, claws and other products often wanted for use in traditional Chinese medicine is banned under a treaty binding 167 countries, including India.
Earlier this year, Singh set up a tiger taskforce along with a National Wildlife Crime Prevention Bureau after a probe found that poachers had killed the entire population of 15 in state-run Sariska National Park.