Elizabeth Mukarugwiza, 37, has Wednesday morning collapsed and died as she tried to sneak into Uganda through the illegal pathways.
Mukarugwiza was a wife to Dan Hakizimana a resident of Nyamirama in Musanza District.
Kigezi Region spokesperson Elly Matte confirmed the incident saying the body was still at Cyanika police by press time.
Matte, said the deceased who was pregnant together with her group had crossed to Uganda when Rwanda security forces started pursuing them.
In the process of running she fell and died on Ugandan soil.
Police is still stuck with the body at Cyanika police in Kisoro District.
Rwanda government earlier warned its citizens against crossing to Uganda. In the process, armed soldiers were deployed to monitor Rwanda border.