Medel lasted only 37 minutes before hobbling off in the Milan derby.
"Scans this morning revealed that Gary Medel has suffered damage to the meniscus in his right knee. An evaluation of his recovery time will be made in the coming days," a club statement said.
It was initially feared that Medel, 29, had damaged ligaments.
Inter coach Stefano Pioli opted on Sunday to use Medel in central defence, a position he believes the Chilean "is perfect for" despite mostly playing as a defensive midfielder since he joined the club from Cardiff City in 2014.
In an entertaining Milan derby that saw Ivan Perisic score a last-gasp leveller for Inter, Medel lasted only 37 minutes before hobbling off to be replaced by Jeison Murillo.
The Chile international could return to action in a matter of weeks, reports said.
Inter, who are away to Hapoel Be'er Sheva in the Europa League on Thursday, are ninth in Serie A, 15 points behind leaders and champions Juventus.