Odeon objects to Walt Disney Pictures' decision to leave only 12 weeks between the film's theatrical and DVD releases in those countries, rather than the usual 17 weeks.
Odeon said it had invested "considerable sums of money" in digital projection equipment to show 3D films, and a shorter window to screen films would undermine its investment.
The company said it feared Disney's proposals would "inevitably set a new benchmark" and a 12-week gap would become common.
Disney said it wants the shorter window in part to fight piracy, but does not plan to introduce it for every film.
Odeon is one of Europe's largest cinema chains, with 110 Odeon and UCI-branded theaters in Britain. Its screens in Germany, Austria, Spain and Portugal will show "Alice in Wonderland" because there is a longer gap between theatrical and DVD release.
Other cinema chains in Britain have expressed disquiet about Disney's move, but so far none has said it will not show the movie.
The Cineworld chain said last week it had reached a "satisfactory compromise" with Disney and would show "Alice in Wonderland" on more than 150 screens in Britain.
Burton's 3D movie stars Johnny Depp, Anne Hathaway and Helena Bonham Carter. It has its world premiere in London on Thursday and opens in Britain and the United States on March 5.