The Cheetham Hill Asda Living store will turn off escalators, screens and music for an hour on Saturday 7 May.
Customers will also be offered a picture map of the supermarket.
General manager Simon Lea came up with the idea after watching an autistic child and his mother struggle on the shop floor.
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"When we open the doors you will be able to hear a pin drop. That's the plan," Mr Lea told the Manchester Evening News.
"I suffered for many years with anxiety and I used to absolutely hate going into busy stores. If we can make a few small changes to give these customers a better shopping experience and make them comfortable then I know the store will be a better place to shop for everyone," Mr Lea said.
The store will open an hour early and no announcements will be made during the quiet hour between 08:00 and 09:00 BST.
Source: The National Autistic Society
Asda said it would monitor feedback from the trial and would consider rolling it out to other stores.
The National Autistic Society (NAS) said it welcomed the move as shops and other public spaces could be "extremely challenging" because of bright lights, strong smells and crowds.
NAS Campaign manager Tom Madders said: "It can cause [autistic people] to feel overwhelmed by 'too much information'. This can be excruciatingly painful or cause extreme anxiety. This may lead to a meltdown or - all too often - people avoid these places and choose not to go out at all.
"Asda's initiative is a great example of an organisation taking the trouble to understand how autistic people experience the world and we hope other retailers are inspired to follow their example."
An Asda supermarket in Manchester is introducing a "quiet hour" to help autistic shoppers who can feel stressed by noise.