This paper presents a simulation study of the wake formation behind a Langmuir probe thinner than the Debye Length in the space environments such as the ionosphere's F region. We find that the wakes formed in plasma density and electric potential behind the positively biased probe can extend up to 15 Debye lengths in the subsonic plasma flow. Higher electric bias and flow velocity can further enhance the plasma wake perturbations. With an external magnetic field parallel to the object's axis, the plasma wake becomes asymmetric and more extensive than for the unmagnetized case. The wing structures in the electron and ion densities are also observed along the background magnetic field in the case of subsonic plasma flow. The quantitative results in this paper may provide a practical reference for data processing and the future design of the Langmuir probe instrument flying in the F region on such as sounding rockets and low Earth orbit (LEO) satellite missions. In particular, since the Langmuir probe instrument may comprise two or more biased Debye-scale Langmuir probes, the plasma wake formed behind a single probe may influence the measurements from other instruments onboard.