Wilson, 77, said he and fellow co-founder Al Jardine have nothing to do with the group's appearance at the Safari Club International Convention in Reno, Nevada.
According to the Safari Club's website, attendees will be able to shop for the latest weapons and organise hunting trips. Trump Jr, a long-time trophy hunter, will deliver the keynote speech.
In a tweet, Wilson said that the gig is being fronted by Mike Love, another Beach Boys founder, who owns the legal rights to the band's name, and will also include longtime member Bruce Johnston.
“It has been brought to my attention that on Wednesday 5 February, The Beach Boys touring group licensed by Mike Love are headlining at the Safari Club International Convention in Reno, Nevada," Wilson said.
He explained that he and Jardine are both “emphatically opposed” to trophy hunting and asked fans to share a petition demanding the Beach Boys pull out of the event.
Addressed to the band's manager Elliott Lott, the petition asks: “Wouldn't it be nice if all the Beach Boys, Stayed away from those who kill for fun?”
The petition also threatens a boycott against the group if they go ahead with the appearance. So far it has attracted more than 65,000 signatures.
It states: “We, the undersigned, pledge to stop buying or downloading all Beach Boys music, going to Beach Boys concerts, and purchasing any Beach Boys merchandise until the Beach Boys withdraw from the SCI Convention and publicly state their opposition to this sick 'sport' of killing animals for 'fun'.
”We will call on the Beach Boys' record label, agent and publicists to disown the Beach Boys, and on members of the public to protest at forthcoming Beach Boys concerts, unless they do so."
Additional reporting by Press Association
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