There are provided a motor control apparatus, an electric power steering apparatus, and a vehicle, capable of controlling the driving of an electric motor accurately even when a failure occurs in a motor electric angle detecting unit that detects a motor electric angle. The motor control apparatus includes: a relative offset amount estimating unit that estimates a relative offset amount between a reference value of an output shaft rotational angle detection value of a steering shaft, detected by an output-side rotational angle sensor, and a motor electric angle original point of a three-phase electric motor; and a motor electric angle estimating unit that calculates a motor electric angle estimate (θme) based on the output shaft rotational angle and the relative offset amount, wherein when at least either one of a resolver and an angle computing unit is abnormal, the driving of the three-phase electric motor is controlled based on the motor electric angle estimate estimated by the motor electric angle estimating unit.