  The search for magnetic monopoles has been a longstanding concern of the
physics community for nearly a century. However, up to now, the existence of
elementary magnetic monopoles remains an open question. The electroweak 't
Hooft-Polyakov monopoles have been predicted with mass at the order of 10 TeV.
This mass scale is unreachable at current colliders. Recently, the muon
colliders have gained much attention in the community due to technological
developments. The advantages of the muon beam encourage us to raise the
high-energy option and consider the high-energy muon collider as a unique
opportunity to search for magnetic monopoles. This letter discusses the
production of magnetic monopoles via the annihilation process and proposes the
search for magnetic monopoles at future high-energy muon colliders.
