The Court of First Instance had examined the accusations leveled against 19 people in the case which has been lodged by Tehran Prosecutor's Office last year. One person was also tried in absentia.
Five of those tried were sentenced to six months in prison, while five others were handed down three-month sentences, said Mostafa Sha'bani, who represents them.
He said the Appellate Court had on Saturday said it had upheld the verdicts during its review of the case, which it carried out last month. Sha'bani said it was not yet clear whether his clients would seek to take the case to the Supreme Court.
The lawyer said four other suspects are clergymen, whose case has been examined by the country's Special Clerical Court.
By lodging the case, the Prosecutor's Office had sought to sue the suspected attackers for disturbing public order, and causing destruction to diplomatic property.
The suspects, however, had the complaint against them about destructive behavior thrown out as such cases have to be lodged with courts by a realtor, namely a legal or natural person with direct interest in the case.
Attackers held violent protests in front of the embassy as well as Saudi Arabia's diplomatic mission in Mashhad in early 2016 against the kingdom's earlier execution of its leading Shia cleric, Sheikh Nimr al-Nimr. Tehran has condemned the attacks, calling its perpetrators rogue elements.
Riyadh reacted to the violence by rupturing its diplomatic ties with Tehran, which it has not restored to date.