The statue was unveiled just last year to honor Reagan and the Polish-born pope, who were both widely credited with helping Poland topple communism 24 years ago.
The vandalism in the Baltic port city was discovered on Tuesday, setting off the search for the perpetrator, said Lucyna Rykowska, a spokeswoman for Gdansk police.
The statue was inspired by an Associated Press photograph taken by Scott Stewart during the pope's second visit to the United States in 1987, and honors Reagan's support for Poland's struggle to end decades of communism.
People interviewed by Poland's TVN24 deplored the vandalism and stressed the popularity of the statue in the park where it is located, saying visitors often leave flowers there.
The damage was initially estimated at more than 100,000 zlotys ($30,000), but the artist who made the statue said it could be repaired within weeks for far less.
On July 17, 2007, Polish President Lech Kaczynski presented his nation's highest distinction, the Order of the White Eagle, to Nancy Reagan on behalf of her late husband.
Poland also has a statute of Reagan in Warsaw, and a roundabout in the city of Wroclaw has been named after him.
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