  We investigate 't Hooft anomalies in the $\mathbb{CP}^{N-1}$ model in
spacetime dimensions higher than two and identify two types of anomalies: One
is a mixed anomaly between the $\mathrm{PSU}(N)$ flavor-rotation and magnetic
symmetries, and the other is between the reflection and magnetic symmetries.
The latter indicates that even in the absence of the flavor symmetry, the model
cannot have a unique gapped ground state as long as the reflection and magnetic
symmetries are respected. We also clarified the condition for the 't Hooft
anomalies to survive under monopole deformations, which explicitly break the
magnetic symmetry down to its discrete subgroup. Besides, we explicitly show
how the identified 't Hooft anomalies match in the low-energy effective
description of symmetry broken phases---the N\'eel, $\mathrm{U}(1)$ spin
liquid, and the valence bond solid phases. An application to the
finite-temperature phase diagram of the four-dimensional $\mathbb{CP}^{N-1}$
model is also discussed.
