Horrified witnesses reported hearing six gunshots being fired outside the superstore outlet in Bangor, Co Down at around 3pm.
They also said the victim had a child with him, although this has yet to be confirmed.
The Police Service of Northern Ireland is appealing for anyone with information on the shooting to come forward.
Detective Sergeant Keith Wilson said: "Police are currently in attendance at an incident in the Balloo Link area of Bangor.
"It is believed that one man has sustained gunshot wounds."
A Sainsbury's spokeswoman confirmed shoppers have been evacuated from the store following the shooting.
She said: "I can confirm there was an incident at our Bangor store and the store is closed while police investigate the matter."
The injured man sustained gunshot wounds in the attack, police said
Brutal act of violence that has no place in Northern Ireland
Northern Ireland Secretary James Brokenshire condemned the attack in a post on Twitter.
He said: "Deeply disturbed by news of the shooting in the Sainsbury's car park in Bangor.
"Brutal act of violence that has no place in Northern Ireland."
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Northern Ireland Secretary James Brokenshire condemned the attack
Steven Agnew, Stormont MLA for North Down, said: "I have heard reports of anything from four to six shots having been fired.
"It's very shocking that this took place in broad daylight on a busy shopping day with children and families present.
"A large number of people will have been shocked by this incident. Anyone who has witnessed or was nearby, undoubtedly, this will live long in their memory."