The dead trainers were identified as Jose Maria Galera Cordoba and Abraham Leoncio Bravo Picallo, both 33 years old. Authorities have not released the name of the translator, reportedly an Iranian-born man with Spanish citizenship.
The trainers were working with a group of 47 Afghan policemen.
'Heart of the problem'
The shooting sparked a large protest outside the camp, with hundreds of people chanting slogans, throwing stones and attempting to storm the Spanish-run base in the provincial capital of Qala-e-Now.
Protesters told the Reuters news agency that the crowd had set fire to one part of the base. One demonstrator, who identified himself as Abdullah, told Reuters that troops inside the base had fired on the protesters.
Mohammad Sadiq, a surgeon at the town's government hospital, said at least 18 wounded people had been brought in for treatment, many suffering from bullet wounds.
Al Jazeera's Hoda Abdel-Hamid, reporting from Kabul, said the shooting "goes to the heart" of the problem confronting coalition forces attempting to rebuild and bring stability to Afghanistan: a huge lack of trust between Nato and Afghans.
"Any kind of little fight could immediately flare up, as we saw today," she said.
The two Spanish policemen were members of their country's Civil Guard, a paramilitary police force similar to Italy's Carabinieri and France's Gendarmerie. Up to 33 Civil Guard officers are deployed in Afghanistan, and the two who were killed Wednesday were scheduled to return home on Friday.