This is early blight of potatoes and is similar to blight on tomatoes. Early blight can attack the vines and tubers. Tubers are frequently infected during harvest from wounding. Spray with a recommended fungicide as soon as spots are observed and repeat at seven- to 14-day intervals for two to three sprays. Do not store infected tubers and remove all plant debris. Do not compost this infected plant material. Avoid overhead irrigation, which may spread the fungus. Maintain fertility in the garden and always purchase disease free seed potatoes.
Contact your local Extension office for a list of recommended chemicals.