The differential multiplicity of dileptons in a hot and magnetized quark-gluon plasma, \(\Delta_{B}\equiv dN_{B}/d^{4}xd^{4}q\), is derived from first principles. The constant magnetic field \(B\) is assumed to be aligned in a fixed spatial direction. It is shown that the anisotropy induced by the \(B\) field is mainly reflected in the general structure of photon spectral density function. This is related to the imaginary part of the vacuum polarization tensor, \(\mbox{Im}[\Pi^{\mu\nu}]\), which is derived in a first order perturbative approximation. The final analytical expression for \(\Delta_{B}\) includes a trace over the product of a photonic part, \(\mbox{Im}[\Pi^{\mu\nu}]\), and a certain leptonic part, \({\cal{L}}_{\mu\nu}\). It is shown that \(\Delta_{B}\) consists of two parts, \(\Delta_{B}^{\|}\) and \(\Delta_{B}^{\perp}\), arising from the components \((\mu,\nu)=(\|,\|)\) and \((\mu,\nu)=(\perp,\perp)\) of \(\mbox{Im}[\Pi^{\mu\nu}]\) and \({\cal{L}}_{\mu\nu}\). Here, the transverse and longitudinal directions are defined with respect to the direction of the \(B\) field. Combining \(\Delta_{B}^{\|}\) and \(\Delta_{B}^{\perp}\), a novel anisotropy factor \(\nu_{B}\) is introduced. Using the final analytical expression of \(\Delta_{B}\), the possible interplay between the temperature \(T\) and the magnetic field strength \(eB\) on the ratio \(\Delta_{B}/\Delta_{0}\) and \(\nu_{B}\) is numerically studied. Here, \(\Delta_{0}\) is the Born approximated dilepton multiplicity in the absence of external magnetic fields. It is, in particular, shown that for each fixed \(T\) and \(B\), in the vicinity of certain threshold energies for dilepton production, \(\Delta_{B}\gg \Delta_{0}\) and \(\Delta_{B}^{\perp}\gg \Delta_{B}^{\|}\). The latter anisotropy may be interpreted as one of the microscopic sources of the macroscopic anisotropies, reflecting themselves, e.g., in the elliptic asymmetry factor \(v_{2}\) of dileptons.