Christopher Ahn was arrested on Thursday in connection with the incident, when a group of at least 10 people stormed into the embassy, restrained and physically beat some personnel and held them hostage for hours in February.
US federal agents also reportedly raided the apartment of Adrian Hong, the leader of self-styled human right group Cheollima Civil Defence, this week in relation to the investigation.
Cheollima Civil Defence, which is seeking to overthrow North Korean leader Kim Jong-un, has claimed responsibility for the incident but denied that they used violence.
Mr Ahn is thought to be the first person arrested in relation to the raid.
A Spanish judicial source said the stolen material has been returned to the North Korean embassy, two weeks after the FBI sent it to the Spanish court investigating the raid.
The incident came just days before the second summit between Donald Trump and Mr Kim, which resulted in a failure to come to agreement about the denuclearisation of the Korean peninsula.
North Korea’s foreign ministry denounced the incident as a “grave terrorist attack” and suggested that the FBI was involved.
The US State Department has denied that accusation.
Cheollima Civil Defence has said the incident was not an attack and claimed it had been invited into the embassy.
“We were invited into the embassy, and contrary to reports, no one was gagged or beaten,” the group wrote on their website.
“Out of respect for the host nation of Spain, no weapons were used. All occupants in the embassy were treated with dignity and necessary caution.”
The group also claimed that the US government was not involved with the incident until after the event.
However, a judge for Spain’s National Court has accused the group of violently beating embassy officials and putting them in “shackles and flanges”.
The judge also said three members of the group took an official into the embassy basement and tried to persuade him to defect from North Korea.
Although documents released by the Spanish court said several members, including Mr Hong, had fled to the United States, their whereabouts are unclear.
The court is seeking their extradition.
Agencies contributed to this report