A raw material gas is supplied to a space in which a silicon carbide seed crystal is placed. A silicon carbide single crystal is grown on the seed crystal by keeping a monosilane partial pressure at 4 kPa or more and heating the space to a temperature of 2400° C. to 2700° C. The temperature of the space and supply of the raw material gas are controlled such that a temperature gradient of a growth crystal surface of the silicon carbide single crystal in a radial direction is 0.1° C./mm or less, and a radius of curvature of the growth crystal surface is 4.5 m or more, thereby producing a silicon carbide single crystal ingot having a growth length of 3 mm or more and an internal stress of 10 MPa or less. The ingot is then cut into a silicon carbide single crystal wafer.