Some 30,500 people, including 17,000 children, have been infected so this year.
Authorities blame a combination of factors including shortages of vaccine and cuts to health services amid an economic slowdown exacerbated by a five-year conflict with Moscow-backed separatists in eastern Ukraine.
Anti-vaccination sentiment, often driven by online campaigns spreading false information about the alleged risks, also plays a role.
The World Health Organization (WHO) recommends a 95-percent vaccination rate to prevent mass hospitalisations and fatalities.
But in Ukraine, just 42 percent of one-year-olds had been vaccinated as of end-2016, according to the United Nations children's agency UNICEF.
Measles cases more than tripled across Europe in 2018, with Ukraine accounting for most of the gain.
Europe as a whole saw nearly 83,000 cases last year, according to WHO figures. The Ukrainian government reported 54,000 cases in 2018.
Measles is characterised by high fever and a reddish rash. It usually triggers only mild symptoms but remains one of the leading causes of death among young children globally.
