Modi, who has put out 101 posts till date, is also the most "effective world leader" on the platform, a conclusion that was reached based on the comments and likes that his posts garner.
The findings are part of a global study, "World Leaders on Instagram", that analysed the activity of around 325 Instagram accounts of heads of state and government and foreign ministers over the last one year.
Trump, who occupies the second spot, has 6.3 million followers while Pope Francis is in third place with 3.7 million followers, ahead of the White House account with 3.4 million followers.
"Leaders around the world are creating online communications that convey global social and political context while also sharing a sense of personality and creativity," said Don Baer, CEO of Burson-Marsteller, in a statement.
Seventy-three heads of state, 38 heads of government and 28 foreign ministers maintain personal pages on the platform, it said.