United boss Jose Mourinho has endured a difficult start to the season, and the Portuguese's task has got no easier after being paired with Italian champions Juventus.
The draw means that Cristiano Ronaldo is scheduled to go up against his former club having left Real Madrid for Turin earlier this summer.
A number of strong teams were potential opponents from pot three, and the two European giants have found themselves paired with Spanish outfit Valencia.
Swiss team Young Boys make up the remainder of Group H, having overcome Dinano Zagreb in the playoff round earlier this week.
The first matchday takes place on September 18 and 19.