The Giallorossi were drawn against the Ukrainian side on Friday night, with the first leg to take place at the Stadio Olimpico.
That game will take place on Thursday 11 March, with the return scheduled for a week later.
After the 5-1 victory over Sporting Braga in the last-32 of the competition, Paulo Fonseca will once again be going up against one of his former sides.
The Portuguese was in the opposition dugout the last time the two sides met: Roma knocking Shakhtar out on away goals in the last-16 of the 2017-18 Champions League.
The Ukrainian side are in the competition after falling out of the Champions League at the group stage - finishing above Inter Milan, but losing out to Real Madrid and Borussia Monchengladbach.
They beat Israeli side Maccaibi Tel-Aviv in the last-32, running out 3-0 winners on aggregate.
The two clubs have faced each other on six previous occasions, all of them in the Champions League. The Giallorossi have won two of those games, losing the other four.
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