This hot-rolled copper alloy sheet contains Mg: 0.2 mass % or more and 2.1 mass % or less, and Al: 0.4 mass % or more and 5.7 mass % or less, with a remainder being Cu and inevitable impurities, among the inevitable impurities, an amount of Fe is 0.0020 mass % or less, an amount of O is 0.0020 mass % or less, an amount of S is 0.0030 mass % or less, and an amount of P is 0.0010 mass % or less, a special grain boundary length ratio (Lσ/L) which is a ratio of a sum Lσ of lengths of grain boundaries with 3≤Σ≤29 to a length L of all measured crystal grain boundaries by an EBSD method is 20% or more, and an average crystal grain size μA in a sheet-thickness central portion is 40 μm or less.