Jose Mourinho's side needed extra time to overcome Anderlecht in the quarters on Thursday night, and travel to Spain in the first leg as they look to lift the Europa League for the first time.
It will be the first meeting between United and Celta in Europe.
Meanwhile, Ajax host Lyon in the first leg on May 4 in the Netherlands before heading to France a week later.
The pair have met on four occasions in the Champions League, drawing 0-0 twice in the 2011/12 group stages, while Ajax ran out 2-1 victors at home and prevailed 2-0 away back in the 2002/03 groups.
Celta Vigo v Manchester United
Read the full article on eurosport.co.uk: Man Utd draw Celta Vigo in Europa League semis, Ajax to play Lyon