Davies suffered medial ligament damage late in the first half of Wrexham’s 4-1 win over Farnborough in the FA Cup last Saturday.
The 24-year-old has scored three goals in 18 games this season for Wrexham, who are currently top of the National League.
“Gutted to pick up the injury on the weekend,” Davies tweeted.
“Will be working hard to be back as soon as possible.”
Davies has been a key player for Wrexham since he rejoined his hometown club following his release by Brighton & Hove Albion in the summer of 2020.
