The Argentinian was carried off on a stretcher in the second half of United's 1-0 derby defeat to City at the Etihad Stadium on Sunday after he mis-judged a sliding tackle and dislocated his left shoulder.
The versatile defender seemed to be in some pain when he was carried off after receiving around two minutes' worth of treatment.
It was something of a surprise, therefore, to see the 24-year-old play down the injury on Twitter the day after the derby.
"Gracias a todos por los mensajes
Gracias a dios fue solo un mal momento/ thank you all for your messages
thank god it was nothing," Rojo wrote.
United believe Rojo, who speaks only limited English as he has only been in the country for just over two months, made something of a mistake in his translation of the Spanish part of his tweet.
"Solo un mal momento" translates as "only a bad moment", rather than "nothing", and the club believe the defender's injury is serious.
Rojo was discharged from hospital on Sunday evening and the club confirmed that the defender had suffered a dislocation.
Medical estimates of a recovery time from such an injury range from six weeks to three months.
In 2011 United defender Rafael was out for three-and-a-half months with a dislocated shoulder.
Although Rojo is yet to convince many he is the answer to United's defensive problems, his absence is a blow to Louis van Gaal.
The United manager is set to be without Phil Jones for some time as the England centre-back is suffering from shin splints - his second injury of the season.
Jonny Evans has not played for over six weeks because of an ankle injury while Chris Smalling will serve a one-match ban for his careless dismissal against City.
That means Van Gaal is likely to field Michael Carrick as a makeshift centre-half alongside either Tyler Blackett or Paddy McNair for Saturday's Barclays Premier League game against Crystal Palace.
One thing in Van Gaal's favour is that behind his makeshift back four he will be able to field arguably the most in-form goalkeeper in the top flight.
David de Gea pulled off some stunning saves to deny Everton last month and he once again proved his worth against City, who could have scored many more had it not been for the Spanish stopper.
De Gea has been very pleased with his recent performances, but he would prefer it if United were winning as well.
"My form is very good
I am playing the best football of my career and I want it to continue, but the most important thing is that we all play well as a team," De Gea told Press Association Sport after the derby defeat.
"The next match is at home and we will train hard all this week to make sure we get all three points."
Van Gaal will not have enjoyed looking at the Premier League table on Sunday night, when United dropped to 10th.
Despite a huge amount of enthusiasm and self-confidence, the fact remains that Van Gaal has endured a worse start to his reign than David Moyes, who was sacked after 10 months last season.
But Wayne Rooney retains supreme faith in the man who appointed him United captain in the summer.
Rooney told MUTV: "We're working on different things, which a lot of us haven't been used to
We're certainly heading in the right direction.
"We're progressing each week and playing some nice football
We need to turn that into results and I'm sure we can do that if we keep working, keep learning and keep doing what the manager wants from us."
Rooney also said Smalling would bounce back from his two careless cautions, which effectively cost United the match.
"Chris is disappointed," the England skipper said.
"It's tough when you get sent off, especially in a derby and with such a long time to go in the game it made it difficult for the rest of us to hold on.
"I'm sure Chris will learn from that."
Source : PA
Source: PA