Last week, Michael Rohana, 24, was charged with theft and concealment of a major artwork, and later released on bail.
The 2,000-year-old statue, worth some USD 4.5 million, is one of 10 on loan to the Franklin Institute in Philadelphia.
The Terracotta Army is one of China's most important archaeological finds.
According to court documents, Rohana was attending an Ugly Sweater Party at the Franklin Institute on December 21 when he made his way into the Terracotta Warriors exhibit, which was then closed.
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He then put his hand on the left hand of the statue and appeared to break something off from it. He pocketed the item and left the museum.
Museum staff noticed the missing thumb on January 8 and the FBI later traced it to Rohana.
Surveillance video and credit-card information established that Rohana had attended the party with five friends from Delaware, authorities said.
He later admitted that he had kept the thumb in a desk drawer.
"We ask that the US severely punish the perpetrator. We have lodged a serious protest with them," said Wu Haiyun.
Wu said the centre would be sending two experts to the US to assess the damage and repair the statue with the recovered thumb. There would be a claim for compensation, he added.
The 10 statues currently on display at the Franklin Institute are part of an army of 8,000 life-size clay warriors which make up the Terracotta Army.
They were discovered in China's Xi'an city in 1974 by a group of Chinese farmers. The museum of the Terracotta Army in Xi'an is now a world famous tourist attraction.
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