Galinski, who has made 51 competitive appearances for the Pilgrims, has switched to Bower Fold in search of regular first team football.
The 21-year-old is expected to make his debut against Oxford City on Saturday.
United will have a 24-hour recall option after the first 28 days of the loan period and Galinski has been granted permission to play for Celtic in the FA Trophy — but not against the Pilgrims if the two clubs are drawn together in the competition.