The uncrewed Chandrayaan-2, which means "moon vehicle" in Sanskrit, was launched at 2:43pm from a tiny barrier island in southeastern India.
India is attempting to become the first nation to land on the south pole of Earth's closet neighbor.
Another failure would have been a further setback to the effort that takes place five decades after men first walked on the moon.
The mission also highlights Indian Prime Minister Narendra Modi's renewed focus on space exploration since he came to power more than five years ago.
Several nations, as well as billionaires Jeff Bezos, Elon Musk and Richard Branson, are competing in an unofficial space race, from launching satellites to sending astronauts and paying tourists into space.
India plans to send a mission to study the sun next year, another to Venus three years later, and eventually establish its own space station.
It is also working on a US$1.4 billion Gaganyaan mission, which aims to put three Indian "gaganauts" -- at least one of whom will be a woman -- into orbit.
The nation, which sent an orbiter to Mars at about a 10th of the cost of NASA's Maven probe, launched a record 104 satellites in 2017.
India is seeking to join an elite club of the former Soviet Union, the US and China in making a soft landing on the moon, in which vehicles touch down without damage.
The spacecraft is scheduled to land in 48 days, officials said.
Two Chandrayaan modules -- an orbiter and a lander -- are stacked together inside a launcher equipped to lift heavy satellites into orbit, while a third module, a lunar rover, is supposed to roll out on landing and operate for at least 14 days on the surface.
The aim is to explore virgin territory on the lunar surface and analyze crust samples for signs of water and helium-3. That isotope is limited on Earth yet so abundant on the moon that it theoretically could meet global energy demands for 250 years if harnessed.
The launch and the satellite together cost 8 billion rupees (US$116 million).
India has specialized in low-cost space launches since the early 1960s, when rocket sections were transported by bicycle and assembled by hand inside St Mary Magdalene Church in Thumba, a fishing village near the tip of the Indian Peninsula.