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.
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Mon, January 16, 2017
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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.
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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."