The Ukraine foreign ministry said in a statement the troops' medical issues related to adapting to the local climate, "general respiratory disease and slight foot and ligament injuries," RIA Novosti reported.
All of the conditions were considered non-life threatening and the soldiers were expected to be released soon, the ministry said.
The exercise, named Rapid Trident, is led by the U.S. Army in Europe and includes at least 16 other countries, including Ukraine, Armenia, Britain, Canada, Sweden and Turkey.
This is the 11th year the exercise had been conducted. It includes weeklong field maneuvers in which a multinational force conducts operations against an imagined enemy.