Five-time winners Bayern will travel to Ukraine in February for the first leg of the tie, in what will be the first ever meeting between the two clubs.
And Ballon d'Or nominee Neuer expects Shakhtar to pose a serious threat to his side's hopes of winning their second Champions League title in three years.
"Donetsk are the great unknowns in the last 16 so preparing for the matches won't be that easy," said the goalkeeper.
"But as always, our coaching and analysis teams will provide us with all the information we need.
"I've never personally faced this team, although I played in Lviv once with Germany when we beat Portugal 1-0 at Euro 2012, so that's a good omen.
"I'm definitely confident we can make the quarter-finals."
Sporting director Matthias Sammer echoed Neuer's confidence around Bayern progressing, but insisted they would not take Mircea Lucescu's team lightly.
"We don't know them," he said. "But any team that makes it through the group stage against the likes of Bilbao has the class.
"We respect Donetsk but intend to progress."
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