Morgan scored 17 in the fifth T20I between England and New Zealand, which was reduced to a 11 overs a side contest due to rain on Sunday, to cross the milestone.
Morgan is only the seventh batsman to reach the milestone of 2000 runs in T20 internationals after Australia's David Warner, former New Zealand captain Brendon McCullum, former Pakistan batsman Shoaib Malik, New Zealand opener Martin Guptill and the Indian duo of Virat Kohli and Rohit Sharma.
Rohit tops the table with 2537 runs while Kohli comes second with 2450 runs to his name.
The England player closest to Morgan is Alex Hales who amassed 1644 runs before his international career came to a halt before the 2019 World Cup. Jos Buttler comes after that with 1260 runs.