Twitter UK published a tweet from their official account on Tuesday saying "name a better footballer than Phil Jones." It was widely condemned by United fans and subsequently deleted.
Sources have told ESPN that after United complained, Twitter later apologised to Jones and the club.
A Twitter spokesperson told ESPN: "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."
Jones, 28, has made 224 appearances in nine years at United after arriving from Blackburn in 2011. He has not travelled to Germany with Ole Gunnar Solskjaer's squad for the final rounds of the Europa League because of injury and last featured for the first team in January.
United play Sevilla for a place in the Europa League final on Sunday and Solskjaer insists his players have got the energy for possibly two more games despite a gruelling season that has lasted more than a year.
"Physically we're fine," said Solskjaer. "All the teams have played many games anyway. but now it's who is the mentally strongest?
"You've got to be strong mentally, concentrated, focused and any of these games can be decided, will be decided, on marginal decisions or finishing.
"So, we've just got to keep them focused and with the right attitude."