Ofcom analysis of 2.3 million tweets in the first half of last season found nearly 60,000 abusive posts, affecting seven in 10 top-flight players.
Half of that abuse was directed at just 12 individuals - eight from United.
However, the study by the Alan Turing Institute also found the vast majority of fans use social media responsibly.
"These findings shed light on a dark side to the beautiful game," said Kevin Bakhurst, Ofcom's group director for broadcasting and online content.
"Online abuse has no place in sport, nor in wider society, and tackling it requires a team effort."