The Central District of Saveh County () is in Markazi province, Iran. Its capital is the city of Saveh.
After the 2011 National Census, the village of Aveh was elevated to the status of a city.
At the time of the 2006 census, the district's population was 215,413 in 57,202 households. The following census in 2011 counted 238,041 people in 68,213 households. The 2016 census measured the population of the district as 259,354 inhabitants in 78,635 households.