Britain's prime minister quickly criticized the execution - China's first of a European citizen in nearly 60 years.
"I condemn the execution of Akmal Shaikh in the strongest terms, and am appalled and disappointed that our persistent requests for clemency have not been granted. I am particularly concerned that no mental health assessment was undertaken," Prime Minister Gordon Brown said in a statement issued by the Foreign Office.
The press office of the Xinjiang region where Shaikh had been held confirmed the execution in a faxed statement.
Shaikh, 53, first learned he was about to be executed Monday from his visiting cousins, who made a last-minute plea for his life. They say he is mentally unstable and was lured to China from a life on the street in Poland by men playing on his dreams to record a pop song for world peace.
Brown had spoken personally to China's prime minister about his case. Foreign Secretary David Miliband also condemned the execution and said there were unanswered questions about the trial.
"I also deeply regret the fact that our specific concerns about the individual in this case were not taken into consideration ... These included mental health issues, and inadequate professional interpretation during the trial," Miliband said in a statement.
China defended the case and criticized Brown's comments, saying drug smuggling was a serious crime.
"We express our strong dissatisfaction and opposition to the British accusation," Chinese Foreign Ministry spokeswoman Jiang Yu told a regular news conference.
Jiang said she hoped the case did not harm bilateral relations, and called on London not to create any "obstacles" to better ties.
Shaikh was arrested in 2007 for carrying a suitcase with almost 9 pounds (4 kilograms) of heroin into China on a flight from Tajikistan. He told Chinese officials he didn't know about the drugs and that the suitcase wasn't his, according to Reprieve, a London-based prisoner advocacy group that is helping with his case.
He was convicted in 2008 after a half-hour trial.
The official Xinhua News Agency quoted China's Supreme Court as saying Tuesday that although officials from the British Embassy and a British aid organization called for a mental health examination for Shaikh, "the documents they provided could not prove he had a mental disorder nor did members of his family have a history of mental disease."
"There is no reason to cast doubt on Akmal Shaikh's mental status," the Supreme Court was quoted as saying.
Xinhua said Shaikh was put to death by lethal injection. China, which executes more people than any other country, is increasingly doing so by lethal injection, although some death sentences are still carried out by a shot in the head.
The Beijing-based lawyer for Shaikh's death sentence review, Zhang Qingsong, said Tuesday he never got to meet with Shaikh despite asking the judge and the detention center for access. He said China's highest court never evaluated Shaikh's mental status.
According to Reprieve, the last European executed in China was Antonio Riva, an Italian pilot who was shot by a firing squad in 1951 after being convicted of involvement in what China said was a plot to assassinate Mao Zedong and other high-ranking communist officials.
"The death of Akmal Shaikh is a sad indictment of today's world, and particularly of China's legal system. ... We at Reprieve are sickened by what we have seen during our work on this case," said Sally Rowen, legal director of Reprieve's death penalty team.
Reprieve issued a statement from Shaikh's family members saying they expressed "their grief at the Chinese decision to refuse mercy."
Associated Press reporters Alexa Olesen and Cara Anna in Beijing contributed to this story.