The two teams will meet for a first-leg last-16 clash in Athens, before playing out the return leg at Old Trafford next month.
Having exited the competition at the same stage to Real Madrid last season, playmaker Kagawa has urged United to claim a positive result against the Greek giants to put themselves in a commanding position.
"When you get to this stage in the competition you can't afford any slip ups or you're out. The away leg is very important – we need to get a good result there. We have a lot of experienced players in our squad who will hopefully help us to achieve that," the Japanese international told the club's official website.
"Our Champions League campaign ended at the last 16 stage last season, so we want to go further this time. Olympiacos are a good team and there are no easy games in this competition - we all know that. We have to prepare as well as we can."
United have won all four of their previous matches against Olympiacos.