The Texas outbreak followed earlier cases in Delaware, New Jersey and Pennsylvania.
However, US government officials said the Texan virus was a different strain from the Asian strand and posed a low health risk to humans.
The EU joins a growing list of importers to place a ban on US product, including Japan, South Korea, Malaysia and Singapore.
Meanwhile, Russia, one of the largest markets for US poultry, and Taiwan have banned imports from Texas only.
The EU ban applies to the import of live birds and eggs from the US.