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."

Defender Terry, 36, is leaving Chelsea this summer after more than two decades at Stamford Bridge.
Swansea, West Brom and Bournemouth have been linked with the former England captain, while a move to China or the United States appear other options.
"I've got options but nothing sorted or in stone," said Terry.
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"Everyone keeps asking me and no-one believes me when I say that I've not got anything sorted."
Terry was an unused substitute in Saturday's 2-1 FA Cup final defeat to Arsenal at Wembley.
He has made 717 appearances for Chelsea and is a five-time Premier League title winner with the London club.
He has also won the Champions League and Europa League, as well as five FA Cups and three League Cups.
Although he has yet to make up his mind whether to retire, Terry is keen to become a manager once he does decide to stop playing.
"I think I've got too much to give and I've learned too much not to pass that on," he added. "I do want to be a manager."
An Asda supermarket in Manchester is introducing a "quiet hour" to help autistic shoppers who can feel stressed by noise.
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John Terry says he has not made up his mind whether to retire from playing and "needs a good week away to reflect" before making a decision.