The social media platform posted a tweet from one of its official handles which read "Name a better footballer than Phil Jones".
It is an account with more than 50 million followers, and Twitter was using the post to test out its new "choose who can reply to a tweet" feature.
Jones has often suffered mocking by opposing fans for his style of play and injury proneness at United.
A Twitter spokesperson said: "Our aim was to showcase our new product feature, conversation controls, which allows you to select who can reply to a tweet.
"It was not our intention to cause upset and once we realised our mistake, we immediately deleted the tweet."