  We show that a topological Nambu monopole exists as a regular solution for a
large range of parameters in two Higgs doublet models, contrary to the standard
model admitting only non-topological Nambu monopoles. We analyze a Higgs
potential with a global $U(1)$ symmetry and a discrete symmetry $\mathbb{Z}_2$.
The monopole is attached by two topological $Z$ strings ($Z$ flux tubes) from
both sides. Despite of a trivial second homotopy group, the discrete symmetry
$\mathbb{Z}_2$ together with a non-trivial first homotopy group for $Z$ strings
topologically ensures the topological stability. After analytically
constructing an asymptotic form of such a configuration, we explicitly
construct a solution of the equation of motion based on a 3D numerical
simulation, in which magnetic fluxes spherically emanating from the monopole at
large distances are deformed in the vicinity of the monopole. Since the
monopoles are expected to be abundant in the present universe, they might be
observed in the current monopole searches.
