Jones withdrew from the Under-21 friendly with Sweden on Tuesday which prompted Pearce to reveal the nature of the 20-year-old former Blackburn player's injury.
However, the problem is evidently not as bad as first feared as Ferguson has named Jones, who can play in defence or midfield, in his squad to face Everton in the Premier League on Sunday.
And Ferguson is not happy with the way the situation has been handled.
"What about doctor confidentiality?" said the United boss."Jones is fine despite what Stuart Pearce says and we're very disappointed with the FA for that.
This is not the first time news of United injuries has emerged from the England camp after senior boss Roy Hodgson claimed winger Ashley Young was missing from a squad earlier this season with a knee problem.
"It is something we have to address," added Ferguson. "The FA is a big organisation, things can leak from a lot of different places. But that was a conversation between our doctor and theirs, and shouldn't have gone any further."
The manager is determined not to witness a repeat of last season's home game against Everton when his side threw away a 4-2 lead in the dying stages of the game to draw 4-4.
"It's a tough game on Sunday. We were 4-2 up with seven or eight minutes to go. It was unexpected and we have to anticipate the unexpected in the run-in. That was a bad blow for us and it cost us the league.
"Everton are very experienced and, if you look at their record, they've only lost three games this season. They're obviously hard to beat.
"But the team is playing well, I'm pleased with their form and I'm pleased that the players we're changing around, when I'm making different team selections, are buying into it well.
"They're all contributing in their own way and that gives us a better chance in terms of dealing with the various competitions we're in now."
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