Michael Rohana, 24, has been arrested over the theft during an after hours "ugly sweater party" just before Christmas at the Franklin Institute in Pennsylvania where 10 of the figures are on display.
According to an arrest affidavit filed by an FBI agent, Rohana snuck into the closed exhibit and snapped a selfie with the warrior, worth $4.5 million.
Rohana then appeared to break off the statue's left thumb and pocket it before leaving the event with friends.
He was arrested for theft of a major artwork from a museum, concealment of a major stolen artwork, and the interstate transportation of stolen property, but released on a $15,000 bail, according to court documents seen by AFP.
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Built around 209 BC to stand guard over the tomb of the first emperor, the 8,000-strong Terracotta Army is one of China's most important archaeological discoveries, and considered a symbol of ancient Chinese artistic and military sophistication.
"We call on the US side to severely punish the person who committed such a damaging act of vandalism and theft of humanity's cultural heritage," the director of the Shaanxi Provincial Cultural Relic Exchange Centre told the Beijing Youth Daily Sunday.
Two experts would be sent to the US to help with repairs, the director said, adding that they had begun the process of claiming compensation for damages.
News of the damage sparked strong criticism on Chinese social media, with many comments nationalistic in tone.
"If they dont understand that our statue is precious why would we lend it to the US in the first place?" another asked.
But a few were more circumspect in their disapproval, recalling China's destruction of its own heritage.
"Who will be held responsible for all the cultural relics destroyed in the Cultural Revolution?" a user wrote, referring to the tumultuous period in the 1960s and 70s when countless artifacts were defaced or destroyed as China tried to rid itself of the influence of traditional culture.
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