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The Giallorossi will travel to Ukraine for the first leg on Wednesday 21 February, with the return leg at the Stadio Olimpico coming on Tuesday 13 March.
As the draw in Nyon progressed, Roma were left with the possibility of facing either Shakhtar or Bayern Munich.
“We have to say that, given who was left available, in the end it went reasonably well for us," club director Francesco Totti said. "But we won’t underestimate Shakhtar in any way: they are a strong side physically and technically.
"Especially at home they are very formidable. It will be a difficult tie and, as we always know, the further you go in the competition the harder the tests are.”
In a post on social media, coach Eusebio Di Francesco reacted to the draw.
"Shakhtar are a strong side, who managed to qualify from a very tough group," he noted. "We earned the right to be in the last-16, and we will do everything we can to continue this adventure."
Shakhtar came second in their group behind Premier League leaders Manchester City - with Napoli forced to settle for third and Feyenoord fourth. Paulo Fonseca's side won all three of their home games in the group stage.
Other than the three sides mentioned above, Roma could also have faced Porto, Sevilla and Basel in the draw.
Sporting director Monchi was pleased to avoid an early rematch with his old club.
"I’ve already said that I didn’t want to draw Sevilla, for a number of reasons," he noted. "We’re up against Shakhtar and we hope for the best."
Elsewhere, perhaps the tie of the round sees Paris Saint-Germain face Real Madrid, while Chelsea - runners-up to Roma in the group stage - will face Barcelona.
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