The association said Wednesday the boycott would have forced it to choose between obeying Ukrainian law or being hit with heavy sanctions from sports bodies.
Ukraine has backed down on a sports boycott of neighboring Russia, a month after banning its athletes from competing there.
The Ukrainian government announced the boycott last month, citing Russian involvement in the conflict in eastern Ukraine and its record of doping in sports, ESPN reported.
However, with the national wrestling team due to compete at the upcoming European championships in Russia, the boycott measure has been changed.
An updated version of the government decree, published last week, says only that the government does not recommend and will not fund the participation of Ukrainians in Russian competitions.
The Ukrainian Wrestling Association said it will take part in the championship in the southern Russian city of Kaspiisk. The event runs from April 30 to May 6.
The association said Wednesday the boycott would have forced it to choose between obeying Ukrainian law or being hit with heavy sanctions from sports bodies.
Read alsoSome EU states may boycott World Cup 2018 in Russia – journalist
Since Russia annexed Crimea from Ukraine in 2014, Ukrainian teams have continued to compete in the country at events in sports such as boxing and biathlon, largely without incident.
The boycott measure, championed by Ukraine's Youth and Sports Minister Ihor Zhdanov, didn't seem to have any effect on several Ukrainian soccer players who represent Russian clubs.
As UNIAN reported earlier, Ukrainian Minister of Youth and Sports Ihor Zhdanov said the ministry had officially barred national teams from taking part in all sports events hosted by the Russian Federation.