Anti-monarchy group Republic launched the petition online, arguing that the "royal wedding is a private, personal event", which is being dressed "as a national occasion."
The group claims that because Eugenie, who is ninth-in-line to the British throne, "carries out no royal duties there is little public interest in another Royal Wedding." They further argue that the monarchy is "forcing another costly ceremony onto the public."
Republic is only 4,500 signatures away from its target of 30,000.
The petition is further calling on the Royal Family to "publish a report of all costs to taxpayers" in a bid for the "highest possible standards of openness and transparency".
A petition on the UK government website needs a minimum of 100,000 signatures before it is debated by MPs in parliament.