  We have investigated the properties of quarkonia in a thermal QCD medium in
the background of strong magnetic field. For that purpose, we employ the
Schwinger proper-time quark propagator in the lowest Landau level to calculate
the one-loop gluon self-energy, which in the sequel gives the the effective
gluon propagator. As an artifact of strong magnetic field approximation
($eB>>T^2$ and $eB>>m^2$), the Debye mass for massless flavors is found to
depend only on the magnetic field which is the dominant scale in comparison to
the scales prevalent in the thermal medium. However, for physical quark masses,
it depends on both magnetic field and temperature in a low temperature and high
magnetic field but the temperature dependence is very meagre and becomes
independent of temperature beyond a certain temperature and magnetic field.
With the above mentioned ingredients, the potential between heavy quark ($Q$)
and anti-quark ($\bar Q$) is obtained in a hot QCD medium in the presence of
strong magnetic field by correcting both short and long range components of the
potential in real-time formalism. It is found that the long range part of the
quarkonium potential is affected much more by magnetic field as compared to the
short range part. This observation facilitates us to estimate the magnetic
field beyond which the potential will be too weak to bind $Q\bar Q$ together.
For example, the $J/\psi$ is dissociated at $eB \sim$ 10 $m_\pi^2$ and
$\Upsilon$ is dissociated at $eB \sim$ 100 $m_\pi^2$ whereas its excited
states, $\psi^\prime$ and $\Upsilon^\prime$ are dissociated at smaller magnetic
field $eB= m_\pi^2$, $13 m_\pi^2$, respectively.
