The ministry spoke out after rumours spread that San Chulanont, Surayud's son, was among members of a yakuza gang arrested in the US on suspicion of trafficking in drugs and weapons.
US authorities revealed on April 7 they had arrested a Japanese yakuza organised crime leader and three Thai men for trafficking heroin and methamphetamine while trying to acquire surface-to-air missiles for rebel groups in Myanmar and Sri Lanka, according to Voice of America.
The US Justice Department said Takeshi Ebisawa, Sompak Rukrasaranee, Somphob Singhasiri and Suksan Jullanan were arrested in New York on April 4 and 5 on suspicion of drug and arms trafficking and money laundering.
Defence Ministry spokesman General Kongcheep Tantravanich said Suksan Jullanan was neither Surayud's son nor a soldier, as rumoured, adding that the suspect has nothing to do with the Privy Council president.
He also claimed that fake news was now being spread widely to defame the ministry.
"Suksan, who holds both Thai and American nationality, is not a soldier and has never been a soldier," he said, urging people not to share the rumour.
Meanwhile rumours that the US had banned Thai imports in retaliation over the case were also fake news, he added.