The bare-breasted protest, by activists from the Ukrainian women's rights group Femen, took place outside the stadium a few hours before European football's ruling body UEFA held the draw for the finals in Kiev.
The group regularly stages half-naked protests in Kiev to highlight what they see as political injustice, social abuse and the exploitation of women in Ukraine.
The young women, who wore only briefs and long stockings, shouted sexually explicit slogans and carried placards condemning UEFA before police could hustle them into a van.
"Today we want football fans and [UEFA President] Michel Platini to forget about playing with their balls because we must be aware of Ukraine's social problems and the fact that Ukraine will become a Euro-brothel," said group leader 22-year-old Olexandra Shevchenko.
"We are sure that UEFA has an interest in the development of sex tourism here and the sale of sexual services during Euro 2012. This tournament is not only about football. It risks being a humanitarian disaster," Femen organiser Anna Hutsol told Reuters.
Femen says its main aims are to improve the role of women in Ukraine's male-dominated, post-Soviet society.
Sex tourists and visiting foreign businessmen who feed Ukraine's sex industry are the group's main targets.
It has also campaigned against sexual harassment of students in universities and railed against international beauty contests such as the Miss Universe competition.
The Euro finals are being co-hosted by Ukraine and Poland, with four playing venues in each. The competition begins in Warsaw on June 8 with the final in Kiev on July 1.
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