Vunipola, whose younger sibling and loose forward Billy underwent knee surgery in November, damaged ligaments in his knee in a European Champions Cup clash against fellow English side Sale last weekend.
McCall, who guided Saracens to European and domestic success last term, didn't definitively rule out the older Vunipola from the Six Nations - England begin the defence of their Grand Slam against France on February 4 - but his prognosis was not good.
"It's not looking good [for Mako] to be honest," said McCall following Saracens' 21-6 victory over Newcastle on Saturday which kept them atop the Premiership standings.
"He's got to go and see his consultant in four weeks' time, and then we will determine how long he will actually be out.
"We have to let the injury settle down as much as possible to have any idea because otherwise you are just guessing.
"It's a big blow to lose Billy and then Mako. "Both are such important players or us.
"We were going to lose them for the Six Nations, but to lose them in the run-up to that is so disappointing."
New Zealand-born Mako Vunipola
has been an integral part of coach Eddie Jones' 13-match winning streak this year.
He played in every Six Nations match as well as starting each of the June Tests - a historic 3-0 whitewash of the Australians in Australia - and the recent games against South Africa, Fiji, Argentina and the Wallabies.
If Mako Vunipola fails to regain fitness Joe Marler is his most likely replacement in the starting XV.