The objective in the present work is to consider a simple example of instability of a conducting self-similar micro jet in the external electric field, which represents a prototype of some microfluidic instabilities. Salt from a point source is emitted into its own aquatic solution, which is subject to an external uniform velocity field together with an electrostatic field, and is convected downstream and diffused. The flow is considered in microscales so that, in contrast to the classical jets, the Reynolds numbers are practically zero, but the Péclet numbers are large. The parameters are found at which such a microjet is unstable. Along with the linear stability analysis, we have fulfilled the numerical simulations of the full nonlinear system of equations. The numerical simulation qualitatively confirmed the results of the linear stability and showed that this instability visually reminds classical instabilities of free jets and wakes.