He is playing his first tournament since suffering serious injuries in a car accident in December 2022 that kept him out of last year's IPL as well as the 50-overs World Cup in India
The 32-year-old is the second man after West Indies' Chris Gayle to reach the landmark in both T20 and one-day international cricket.
The RCB captain got to the mark after pulling Jasprit Bumrah for six in his knock of 51 from 42 balls, joining Gayle, Keiron Pollard, Shoaib Malik and David Warner as the other players to have scored 10,000 runs in the shortest format.
Kohli has a total of 10,038 runs from 314 games at an average of 41.65 in T20s, with 3,159 of those coming while playing for India. He has scored five hundreds in the format, all for RCB.