Microquasars are expected to emit high-energy γ-rays owing to their general similarities to γ-ray-emitting blazars (evidence of relativistic jets, non-thermal radio to X-ray emission). In fact, the first source of this type, Cyg X-3, has recently been unambiguously discovered by satellite telescopes. We study the features of the γ-ray radiation produced in these sources by relativistic electrons accelerated in the inner part of the jet. The electrons initiate an inverse Compton e± pair cascade in the radiation field of the accretion disc. Owing to the anisotropy of the accretion disc radiation field, the spectra of γ-rays show a strong dependence on the observation angle, the location of the emission region within the jet, and the details of the acceleration process. As an example, we test our model with observations of the microquasar Cyg X-3, which has recently been reported as a transient GeV γ-ray source by the Agile and Fermi observatories. Satisfactory descriptions of the γ-ray spectra observed from Cyg X-3 are obtained in the case of injection of electrons in the inner part of the jet (located within 300 inner disc radius from the jet base), provided that the observer is located at a relatively small angle to the jet axis.