The supermarket has launched an investigation and recalled the product from its stores.
A spokesman said: "As a precautionary measure, we are recalling the above product as there is a very small risk that some packs may contain pieces of metal."
The two separate incidents occurred in Machester and Glasgow, over 200 miles apart.
One of the women only discovered the metal when it stabbed her gum as she ate.
Both packs were purchased over the Easter weekend and the recall relates to 170g packs of trimmed beans with 'display until' dates of 22nd April, 23rd April and 24th April.
Any packets found should be returned to Morrisons for a full refund.