The lowest category storm that can potentially cause damage to shingles or a roof is typically a Category 1 hurricane. While Category 1 hurricanes are the least intense on the Saffir-Simpson Hurricane Wind Scale, they can still produce sustained winds of 74-95 mph (119-153 km/h), which can lead to some damage, particularly to roofs, shingles, and other structures. Therefore, the answer is:
Category 1