The clashes erupted Thursday in an area about a mile (1.6 kilometres) from the Kenyan border, between the Borana and Garri tribes over a land dispute, the Kenya Red Cross Society said in a statement.
The Ethiopian government said the spat was over "administrative claims" by the two sides.
"The local authorities were not able to resolve the claims and counterclaims in a constructive manner so clashes ensued," Ethiopian government spokesman, Bereket Simon said, without giving details on the toll.
Bereket said police had made several arrests.
"Federal police and government have intervened and all the culprits are under control," he said, adding that the situation has now "normalized."
According to the KRCS statement, "at least 18 deaths and 12 injuries had been confirmed" and the conflict has also led to "loss of properties with reports of massive displacements of populations" into neighbouring Kenya.
KRCS says a registration to determine the actual displaced populations was ongoing but said "more than 10,000 people require urgent humanitarian support".
Bereket said the displaced people were expected to return to Ethiopia shortly.
"This is a hiccup which we are going to address and they will be back soon ... and will continue to live their normal lives," he said.
Moyale is in Oromia region in Ethiopia. Several pastoral tribes occupy the southern part of the region - routinely hit by drought - and rely on land for animal grazing.