The Chelsea left-back, who is on loan at Schalke this season, sustained the injury in Ghana's 1-0 win over Uganda on Tuesday.
He was substituted in the first half and underwent tests in the Gabonese capital of Libreville on Wednesday.
Diego Costa snapped training on his own at Chelsea
Mon, January 16, 2017
Express Sport brings you all the best snaps as Diego Costa is pictured training on his own at Chelsea
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Diego Costa has been pictured training on his own
A statement released by the Ghana football association said Rahman had suffered "a rupture of the meniscus and a particular tear of the anterior cruciate ligament with fluid collection in the left knee."
And 22-year-old will fly to Germany later today for more tests and with surgery a possible option.
Baba Rahman suffered the injury playing for Ghana
Rahman joined Chelsea from Bundesliga side Augsburg for an initial £14million in August 2015 on a five-year deal.
But he made only 15 Premier League appearances under Jose Mourinho and his successor Guus Hiddink.
Baba Rahman joined Chelsea in 2015
Rahman was sent away on loan by Antonio Conte after the Chelsea boss deemed him to be too attack-minded.
Rahman said in August: " Conte told me that he wants his team to be very defensive, but I am a rather offensive full back.
"So I would have had very little playing time. Conte advised me to leave on loan. We will see what happens after this season."