The council gave the go-ahead for the £150m project at East Tullos last week.
The incinerator would be used by Aberdeen, Aberdeenshire and Moray councils for non-recyclable waste, to reduce the amount sent to landfill.
Four community councils raised concerns, but the Scottish government said it did not consider the proposal raised issues of national significance.
The project is designed to generate heat that would be used in thousands of nearby homes.
It was given the go-ahead by the full city council  - by 23 votes to 14 - despite opposition from campaigners who said it could cause problems with pollution and increase traffic congestion on the already busy Wellington Road.
The plant is due to open in 2021.
A controversial £150m energy from waste plan in Aberdeen will not be called in the Scottish government.