Aldi has also pledged to implement additional inspection procedures at their warehouses and stores, the Milwaukee Journal Sentinel reported.
"At Aldi, we are committed to providing high quality products," the company said in a statement. "We sincerely regret any inconvenience or concern this situation may have caused."
Yvonne Duckhorn was shopping at an Aldi store Thursday when she said she found the spider in the grapes.
"I saw the legs moving frantically," Duckhorn said. "I've seen bugs on fruit before, and I thought, 'That is a very big spider.' Nothing I'd ever seen before."
Black widow spiders build webs in grape vineyards to trap insects, and they have been found in supermarkets occasionally since the 1990s.
In the past few months, black widows have been found in Michigan, Missouri and Minnesota.