The quantum vortices formed as a result of barrier-suppression ionization of a two-dimensional hydrogen atom by an ultrashort laser pulse are theoretically investigated. Using an analytical expression for the wave function of a photoelectron in the momentum representation, the probability flux density is investigated. In this case, both the standard definition of a flux and an alternative “symmetrical” one are used. The latter, due to the sensitivity to the phase of the wave function, makes it possible to identify quantum vortices in the momentum space.