U.S., France, Colombia, Philippines and Australia are the finalists.
The uproar began in June when Donald Trump, then co-owner with NBC, made anti-immigration remarks that offended Mexicans.
Spokesman Michael Cohen confirmed that Trump purchased NBC's half of the Miss Universe Organization.
"Miss Universe has existed before this gentleman (Trump) owned the pageant and will continue to exist when he leaves. I will not change everything that is happening in my life just because of a presidential campaign," said Paulina Vega.
Panama joins Mexico and Costa Rica in boycotting Miss Universe pageant after Trump's controversial comments on Mexican immigrants.