OAK BROOK, Ill.—McDonald’s Corp. is freshening up the Quarter Pounder.

By May, quarter-pound burgers at McDonald’s restaurants in the contiguous U.S. will be made from fresh beef. The move to please customers who want less processed food will make supplying some 14,000 U.S. restaurants more complicated at a time when McDonald’s is also trying to position itself as the go-to chain for cheap breakfasts and sandwiches. In January, McDonald’s said changes to its value menu helped boost same-store traffic in 2017 for the first...