England coach Andy Flower revealed on Saturday that both batsman Pietersen and wicketkeeper Prior are to have scans on their right knee and left calf respectively, after suffering discomfort in the tour match against Australia A in Hobart.
Additionally, Pietersen - who spent three months out with the same injury earlier this year - is to have a cortisone injection and on Sunday flew not with his team-mates to Sydney for their final warm-up match but for expert medical opinion and treatment in Melbourne.
However, by early afternoon local time he was able to tweet: "I AM FINE", followed by '£relax'.
Pietersen gave no further context to his message for his many followers - but after the bombshell about his injury, only 12 days before the start of the Ashes, it appears to refer to the injury.
Anderson is also positive about the 33-year-old's fitness ahead of this week's four-day warm-up match against a New South Wales XI, and also the first Test which starts on November 21.
He told Sky Sports News: "I think Kevin's gonna be fit for the game on Wednesday, which is good news.
"And Matt, I think it was a precaution he didn't keep in the last game, and we've got our fingers crossed he'll be fit for the first Test."
Anderson believes it is sensible practice for England not to take any undue risks with their players.
"It (managing injuries) is something the management do with all the players, they try and look after them and rest them when they need to and just take precautions when they need to," he added.
"We've got a long five Tests ahead of us and we need Kevin for all of them if we can, so looking after them now is crucial."
England spinner Graeme Swann was in similarly positive mood about Pietersen and Prior.
He said: "There were some very slight concerns last night but we woke up to very good news this morning.
"Kev's had an injection and should be fit for Wednesday, and Matty Prior as well, he'll bounce back and be ready in a couple of days.
"Luckily it's happened to two of the fittest members of the squad.
"Even though they're two of the older guys, they're two of the guys who keep themselves in the best nick so they'll bounce back in no time."
Meanwhile, Cricket Australia has confirmed that captain Michael Clarke and pacemen Ryan Harris and Peter Siddle will continue their preparations for the first Ashes Test at the high performance facility at Allan Border Field in Brisbane, sitting out the third round of the Sheffield Shield as they work their way back to full fitness.
Australia will name their squad for the opening Test on Tuesday.