The LVM3-M6 rocket launched the US-built AST SpaceMobile communications satellite into low-Earth orbit.
The Indian Space Research Organisation (ISRO) said it was the "heaviest payload to be launched from Indian soil".
The launch is a boost for India's ambitious low-cost space programme, with plans for an uncrewed orbital mission and human spaceflight in the coming years.
The satellite, weighing 6,100 kilograms (13,448 pounds), was launched on a modified version of a rocket that India plans to use for its future space missions.
India is vying for a larger slice of the booming commercial satellite business as phone, internet and other companies seek expanded and more high-end communications.
Modi said the launch marked "a proud milestone in India's space journey".
"It strengthens India's heavy-lift launch capability and reinforces our growing role in the global commercial launch market," he said in a statement.
Earlier this year, ISRO launched the CMS-03 communication satellite, which weighs about 4,410 kilograms.
For these heavy launches, India has deployed an upgraded version of the rocket it used to send an unmanned craft to the Moon in August 2023.
The world's most populous nation has flexed its spacefaring ambitions in the last decade with its space programme growing considerably, and rivalling the achievements of established powers at a much cheaper price tag.
It has said it plans to launch an uncrewed orbital mission before its first human spaceflight in 2027.
Modi has also announced plans to send an astronaut to the Moon by 2040.
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