James Gallivan posted a picture on Facebook as a queue of motorists desperate for a caffeine hit snaked out of Snowhill Retail Park.
The popular coffee chain had previously closed all 2,700 of its stores as part of the UK's lockdown.
Costa confirmed on social media on Friday that Snowhill would be open for drive-through and delivery only.
Mr Gallivan posted on Saturday afternoon: "Just been up to Snow Hill for some shopping from Iceland.
"We had to Queue for 10 mins just to get onto the retail park to only see the whole queue was for Costa Coffee!! On way out the Queues had got even worse, right back to The Vine Tree (Capri) roundabout!!!
"The road was in chaos, a police car couldn't even get through at one point!!
"Seriously people of Wakefield give your head a shake if a coffee is that important to you, WE ARE ON LOCKDOWN!!!!!
"Carrying on like this we will never get rid of this Virus, pure madness!!!!"
Costa said the Leeds Crown Point outlet would also be open, but for delivery only.
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