Sowmaeh District () is in Torkamanchay County of East Azerbaijan province, Iran. Its capital is the village of Sowmaeh, whose population at the time of the 2016 National Census was 2,432 people in 791 households.
In 2024, Torkamanchay District was separated from Mianeh County in the establishment of Torkamanchay County and renamed the Central District. The new county was divided into two districts and five rural districts, with Torkamanchay as its capital and only city at the time.