The CSKA Moscow shot-stopper was struck in the head by a flare in the opening seconds of Russia's Euro 2016 qualifier against Montenegro on Friday.
Akinfeev was taken to hospital, with the clash eventually abandoned during the second half after multiple incidents.
Russia team doctor Edward Bezuglov said in a statement that Akinfeev was diagnosed with concussion and neck burns.
The 28-year-old will return to Moscow with the rest of the squad to continue his treatment.
According to reports, Russia have lodged a protest to UEFA after wanting the clash abandoned following the incident involving Akinfeev.
The match continued until the 67th minute, when Dmitri Kombarov was apparently hit by a coin, with the score at 0-0.
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