Rybka, 24, failed a doping test following a league game against FC Karpaty on November 27 after UEFA representatives paid an unscheduled visit to Shakhtar's training camp.
Rybka, capped once after making his international debut in a friendly against Estonia last year, had been in contention for a place in Ukraine's squad for Euro 2012 which the country will co-host in June.
"According to official documents [from UEFA], the goalkeeper of our team has been disqualified for two years," the club said in a statement on their website.
"From the point of view of Shakhtar club, this is an extraordinarily harsh sentence which does not reflect the scale of the footballer's offence. Consequently, Shakhtar will be appealing to the relevant UEFA bodies," the statement said.
If the ban is upheld, Rybka will not be eligible to play in the Euro tournament. Donetsk, the mining city where Shakhtar are based, is one of four host cities in Ukraine, which is co-hosting the event with Poland.
The club's general manager, Sergei Palkin, was quoted earlier this month as saying that Rybka had taken a diuretic to lose weight but had not consulted the club's doctor before doing so.
Shakhtar have brought back their former reserve keeper Bohdan Shust from fellow Ukrainian Premier League side Illichevets Mariupol to cover for Rybka.
Rybka's positive test was the second major blow to Shakhtar's hopes of retaining their Ukrainian league title this month.
Their long-serving Romanian coach Mircea Lucescu broke seven ribs and suffered concussion in a car crash in Bucharest in early January and has still not returned to Ukraine.
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