The official reportedly denied involvement until he was confronted with the video and then produced the missing wallet.
Pakistani officials at first refused to tell their guests who the culprit was, until the furious Kuwaitis insisted and were shown the film.
Sources in the ministry told the paper an internal inquiry was now underway against the bureaucrat and further action would be taken according to its conclusions.
Pakistan's new prime minister, Imran Khan, has long pledged to clean up government and has for years railed against the graft and corruption among senior politicians and officials.
When questioned about the incident, Fawad Chaudhry, information minister, told a press conference that most of the civil service had their "moral training" during the previous governments.