Judge Mohammad al-Baadani ordered the release of three of the accused who have been in detention since March 2003, they said on Monday.
Charges were also dropped against the main accused, Ali Rashed al-Saadi, being tried in abstentia, they said.
Prosecutors had demanded the maximum penalty of 10 years imprisonment for the four who were accused of being agents of the government led by the former Iraqi president Saddam Hussein.
The four men were accused of having several suitcases of TNT in their Sanaa flat allegedly destined for use against Western embassies in Yemen around the time of the US-led invasion of Iraq in March 2003.
The trio who were in custody had repeatedly protested their innocence since going on trial in August and strongly deny having worked as agents of the former government.
The court, which was due to deliver its verdict on 11 October, decided to hold a session on Monday because the Muslim holy month of Ramadan starts on Tuesday or Wednesday.