Chaplow arrived at The Den almost a month ago from Southampton on a deal until the end of the season.
His absence will come as a major setback for Kenny Jackett's team as they prepare for the FA Cup semi-final with Wigan this weekend.
A brief statement from Millwall read: "Scan results have confirmed that midfielder Richard Chaplow will miss the remainder of the season."
Chaplow verified his position on a social network site, where he said: "Bad news regarding the ankle.
"Six to eight weeks I've been told. I would like to thank Millwall FC for the opportunity. Sorry it ended with injury."