Davies suffered a dead leg during the Scarlets' controversial defeat at the hands of Ulster two weeks ago and has failed to recover in time.
"Jon's looking very doubtful, his dead leg is taking a long time to heal and it could be one to four weeks out," said Scarlets head coach Nigel Davies.
"To have Jon in the mix would be great but we have other good centres and Sean Lamont can also play there."
Davies has been the in-form Welsh centre this season and was ever-present during the Dragons' Six Nations campaign.
But the news will be softened by the return of fit-again international trio George North, Stephen Jones and Sean Lamont to face Tony McGahan's men.
North has been sidelined with concussion since the league clash with Benetton Treviso, Lamont with a hamstring strain which has kept him out of action since the RBS 6 Nations, while Jones looks to have recovered from the wrist injury that forced him off against Ulster.
"Stephen should be okay and George and Sean are also both fine," added Davies.
Munster need just one more win to secure top spot in the Magners League while just two points will see them earn a definite home semi-final.
But the Scarlets are fighting for their own play-off hopes and need to win their remaining three games as well as other results going their way to sneak into the top four.
"Munster are such a quality side, they're used to winning and have that mentality bred into them.
"They're top and will want to come here and continue their fine league form. I wouldn't be surprised if they come with their first choice side.
"It is simple for us we have to win our three games to have any chance of qualifying. We have to be up for the challenge."
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