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The facility is located in Lviv, about 70km from Poland, and primarily manufactures paper bags.
Around 100 people are employed at the plant.
Mondi said that its integrated pulp, uncoated fine paper and packaging paper mill facilities in Russia have remained operational.
Russia represented around 12% of the group’s sales by location of production last year.
The country has also generated around 20% of the company’s underlying earnings before interest, tax, depreciation and amortisation (EBITDA) over the last three years.
In a statement, Mondi said: “The humanitarian crisis unfolding in Ukraine is of great concern.
“Our thoughts are with all those impacted by these tragic events, including some of Mondi’s employees.
“Our businesses primarily serve the domestic Russian market and have continued to operate through this time of heightened geopolitical tension.
“We are actively monitoring this rapidly evolving situation, the international response and the implications for the Group.”
Mondi operates facilities in Syktyvkar, Peraslavl, Aramil and Lebedyan, employing a total of 5,300 people across Russia.
In a separate development, the company has reported full-year revenues of €7.72bn ($8.56bn) for the fiscal year 2021 (FY21), representing a 16% growth from €6.66bn ($7.38bn) in 2020.
Mondi said the growth in revenue was driven by a combination of increased sales volumes and higher selling prices.
During the 12 months to 31 December, the firm’s underlying EBITDA increased to €150m ($166.35m), up by 11% from a year earlier.
On 1 March, French glass container manufacturer Verallia suspended production at its facility in Zorya, Ukraine, amid Russia’s invasion.
Located in Ukraine’s western region, the site supplies half its total output to domestic customers and exports the rest across Europe.