The human rights group has called for urgent reform of law enforcement agencies and has urged caution to football supporters travelling to the country in the summer
In a report released on police brutality in the country, the human rights group cited the case of two men who were beaten by police officers in the city of Lviv in April.
"The Ukrainian government must take action now to stop widespread police criminality," Amnesty director John Dalhuisen said.
“Failure to do so will encourage them to continue acting as a law unto themselves and put Euro 2012 fans in danger from a force that is out of control.”
Ihor Savchyshyn and Andrei Semenyuk were arrested in Lviv following a disagreement in a bar and were subjected to a brutal assault and robbery by six police officers on April 21.
Local prosecutors refused to open a criminal case against the officers until the victims’ lawyer gave an interview to a local television channel.
Amnesty alleged there were numerous such cases in Euro 2012 host cities in which police have tortured people in an attempt to extort money, extract a confession, or simply because of the victims’ sexuality or ethnic origin.
The report is another blow to Ukraine's image abroad, which has suffered recently due to the alleged mistreatment of jailed opposition leader Yulia Tymoshenko.
EU Commission President Jose Manuel Barroso and Justice Commissioner Viviane Reding have announced they will boycott Euro 2012 in protest.
Ukraine will host 11 matches during the tournament in the cities of Kiev, Lviv, Donetsk and Kharkiv.