Saturday's Twickenham final kicks off at 1700 BST, which ranges between 0200 and 0500 in New Zealand and Australia.
The petition on Change.org, entitled "Change the kick-off time of the Rugby World Cup final" and seemingly initiated by the "Green and Gold Rugby" website, had 450 signatures on Wednesday morning.
"After weeks of little sleep with games in the middle of the night, it's only fair the governing body listen to the rugby global powerhouse of the southern hemisphere and push it back to a more suitable viewing time for fans of the competing teams," the petition said.
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"The southern hemisphere teams have given English audiences the greatest gift of all -- the gift of dominant running rugby and rolling mauls. All we ask in return is a small change of schedule. By playing the game a mere seven hours earlier you will be making us, your rugby superiors, very very happy.
"It's not as if UK fans are that interested in the final since their teams are out, so get on board this worthy cause."
Many of the tournament's most high-profile matches have kicked off at 8pm local time but organisers said the final kick off time was decided two years ago after a widespread consultation exercise.
(Editing by Sudipto Ganguly)
