Chopra, 26, was forced off after 30 minutes after a heavy challenge from Doncaster's Wayne Thomas.
"When the swelling goes down, we'll reassess it and see what needs to be done," said Cardiff manager Dave Jones.
"Hopefully we'll just leave it and it will heal naturally itself. If not, [the medical team] will pin it and that will add two or three weeks to the recovery period.
"But we're shooting a little bit in the dark until the 10 days are up and the specialist sees him. But we're looking at a minimum of eight to 10 weeks certainly.
"It's a blow to us because he's a vital cog in our wheel and what we are trying to do. We don't want to lose any of our good players, but somewhere along the lines we will.
"The good thing this year is we've got good players to come in."
Cardiff's impressive victory over Doncaster came at a price as Chopra was joined in the Bluebirds treatment room by defensive pair Kevin McNaughton and Darcy Blake.
Scottish full-back McNaughton limped off in the 18th minute after pulling up sharply with a hamstring strain and was replaced by debutant left-back Lee Naylor.
McNaughton will miss Saturday's Championship trip to Portsmouth, but manager Dave Jones hopes to have available for selection after next week's international break.
Jones also confirmed Wales international Blake "rolled his ankle" in the warm-up and was replaced in the starting line-up by teenager Adam Matthews.
Source: BBC Sport
Source: BBC Sport