He last represented the Kiwis in the 2017 Champions Trophy.
Moeen contributed with both bat and ball.
The pacer will be available for the remaining 9 matches this season.
Root remained unbeaten on 51 off 22 deliveries.
In order to add stability to the middle-order, they felt the need to rope in a hard-hitting batsman for the T20 action.
The Australian opener last played for the national side in the year 2016.
The tradition of hosting the Mascot Derby during every finals day of the tournament started in 2004.