The Indian space agency said the engine was fired for 240 seconds at ISRO Propulsion Complex in Mahendragiri, Tamil Nadu
Mr Musk, a lifelong space enthusiast who aims to make humans a multi-planetary species, founded SpaceX in 2002 with an aim to bring down the cost of space transportation. His company pioneered reusable rocket technology to achieve that goal.
Despite being competitors, Mr Musk has often praised ISRO's efforts to achieve big with minimal cost. When ISRO launched 104 satellites on a single rocket in February 2017, Mr Musk said he was very impressed by the record-breaking feat.
India's Gaganyaan Mission was initially set to be launched in 2022, but it's not clear if the deadline will be met because of the coronavirus pandemic. The mission's objective is to demonstrate India's capability to send humans to low earth orbit in an Indian vehicle -- the heavy-lift GSLV Mk III -- and bring them back to Earth.
There's also a huge commercial interest in space travel. Recently, billionaire entrepreneur Richard Branson flew to the edge of space for a test flight and Amazon CEO Jeff Bezos is set to fly to space later this month.