Scientists, clapping and cheering, tracked the ascent on computer screens.
"This is a historic moment for India," Indian Space Research Organization chairman G. Madhavan Nair said.
"We have started our journey to the moon and the first leg has gone perfectly well," he said, adding that they hoped to "unravel the mystery of the moon."
The moon mission comes just months after it finalized a deal with the United States that recognizes India as a nuclear power.
"It is a remarkable technological achievement for the country," said S. Satish, a spokesman for the Indian Space Research Organization, which launched the 3,080-pound satellite from the Sriharikota space center in southern India.
To date only the United States, Russia, the European Space Agency, Japan, and China have sent missions to the moon. The United States is the only nation to have landed a man on the lunar surface, doing so for the first time in 1969.
In 2003, China became the first Asian country to put its own astronauts into space. It followed that last month with its first spacewalk.
Last year China also blasted an old satellite into oblivion with a land-based antisatellite missile, the first such test ever conducted by any nation.
The head of India's space agency says it can quickly catch China, its rival for Asian leadership.
"Compared to China, we are better off in many areas," Nair said in an interview with India's Outlook magazine this week, citing India's advanced communication satellites and launch abilities.
