The three allegedly crossed over to Uganda before breaking into a shop at Kukokye trading center.
A mob in Kabale district has lynched three Rwandans on suspicion of being robbers.
The deceased are Allen Bampolikyi, Alexander Munyankinde (also known as Rasta) and Moses Ndimubanzi (aka Moshi).
They hailed from Nyakagarama village, Rukoma parish in Nyakatare sub-county in neighbouring Rwanda.
They allegedly entered Uganda through Kahondo parish in Maziba, Kabale, before breaking into Saverina Nyanzigye's shop at Kukokye trading center Saturday night.
Reports show that the three men stole 25 kilograms of maize flour, three boxes of African gin, one box of coffee spirit, some mattress and plastic chairs.
But they were reportedly spotted by a group of residents who pursued them and caught them on the Rwandan side of the border before lynching them.
Elly Maate, the Kigezi region police spokesperson, condemned the mob justice, adding that the police visited the scene of the killings.
He said the owner of the shop, Saverina Nyanzigye, was arrested for questioning as inquiries into the matter continue.