The 22-year-old centre-back was ruled out for the remainder of 2014 after dislocating his shoulder for the second time this season in a training session on Monday.
Papadopoulos, who is on a season-long loan at the Bay Arena from fellow Bundesliga side Schalke, has now gone under the knife as he starts his recovery.
"Kyriakos Papadopoulos underwent successful surgery on Monday evening in Herne on his shoulder," Leverkusen posted on Twitter.
Speaking before Leverkusen's visit to Zenit for their UEFA Champions League clash, Bayer's sporting director Rudi Voller expressed his sadness at Papadopoulos' setback.
"It's a really bitter blow for us and, above all, for him," he said. "He was just getting up to speed."
Papadopoulous has been restricted to just four Bundesliga appearances for Leverkusen.
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