The items – mostly Mamia branded nappies from discount supermarket Aldi – were taken from six pallets at the Scene food bank in Mocha Parade at some point between Tuesday 14 August and Friday 17.
Greater Manchester Police are investigating the theft, which Superintendent Howard Millington said has “shocked even the most unshockable” of its officers.
He added that stealing nappies from a food bank was “beyond low”.
“This food bank is there for the community when they need it most, and many of the items donated come from people within that same community,” he said.
“In Salford we look out for each other, and sadly we are all victims of this robbery.
“We have already had people come forward with information to try and help us with our investigation, we are very grateful for this and hope it continues.
“We are determined to find those responsible for this inexcusable crime, so anyone with any information is asked to call police as soon as possible.”
Manchester Evening News reported that the stolen goods had been due to be distributed to people in need on Monday.
According to the newspaper, the same thieves also attempted to break into a food bank next door, but could not force their way inside.
:: Anyone with any information is asked to contact police on 0161 856 1319, alternatively call police on 101 or call the independent charity Crimestoppers on 0800 555 111.