Chandrayaan-1 (Moon vehicle), a cuboid spacecraft built by the Indian Space Research Organisation (ISRO) blasted off from a southern Indian space centre shortly after dawn in a boost for the country's ambitions to gain more global space business.
Chinese astronauts were feted as national heroes last month after their country's first space walk, and India did not want to be left behind.
"What we have started is a remarkable journey," G. Madhavan Nair, chairman of ISRO, told reporters.
India's national television channels broadcast the event live. Some scientists thumped their chests, hugged each other and clapped as the rocket shot up into space.
Greeted with patriotism in the media, the launch appeared to have helped India regain its self-confidence, which has taken a beating in recent weeks amid signs of an economic slowdown.
"Destination Moon ... Historic Day For India" blazed one TV channel on its screen.
Barring any technical failure, the spacecraft will reach the lunar orbit and spend two years scanning the moon for any evidence of water and precious metals.
A gadget called the Moon Impactor Probe will detach and land on the moon to kick up some dust, while instruments in the craft analyse the particles, ISRO says.
A principal objective is to look for Helium 3, an isotope which is very rare on earth but is sought to power nuclear fusion and could be a valuable source of energy in the future, some scientists believe.
It is thought to be more plentiful on the moon, but still rare and very difficult to extract.
The project cost $79 million, considerably less than the Chinese and Japanese probes in 2007 and ISRO says the moon mission will pave the way for India to claim a bigger chunk of the global space business.
The mission is also expected to carry out a detailed survey of the moon to look for precious metals and water.
FROM NUCLEAR POWER TO SPACE POWER
For many Indians, the launch is another notch in India's ambitions to be a global player. India recently signed a civil nuclear deal with the United States, effectively making it a defacto nuclear power.
In April India sent 10 satellites into orbit from a single rocket, and ISRO says it is planning more launches before a proposed manned mission to space and then onto Mars in four years time.
ISRO is collaborating with a number of countries, including Israel on a project to carry an ultra-violet telescope in an Indian satellite within a year.
It is also building a tropical weather satellite with France, collaborating with Japan on a project to improve disaster management from space, and developing a heavy lift satellite launcher, which it hopes to use to launch heavier satellites by 2010.
India has launched 10 remote sensing satellites since 1998, has several broadcast satellites in space to control 170 transponders and has also launched light-weight satellites for Belgium, Germany, Korea, Japan and France.