The woman, a former State Department employee now living in Sweden, was charged on Thursday, and news of her husband's identity surfaced on Friday.
The acts of espionage were carried out while the two were married.
Sweden's Ministry of Foreign Affairs spokeswoman Charlotta Ozaki Macías confirmed that the ministry had been aware of the case for years.
"The Foreign Ministry official with a connection to the case is not guilty of criminal activity," she told the TT news agency.
The Swedish man remains in service at the ministry.
In a statement, US justice officials said that the woman, 55-year-old Marta Rita Velazquez, allegedly helped to "spot, assess and recruit US citizens" in sensitive national security positions to serve as Cuban intelligence agents.
A native of Puerto Rico with an Ivy League education, Velazquez worked for the US State Department's international development arm USAID from 1989 until 2002 when she left the country and never returned, the Justice Department said.
A grand jury returned an indictment against her in February 2004, but it remained sealed until it was opened Thursday in US District Court in Washington.
The Justice Department said Velazquez, also known as "Marta Rita Kviele" and "Barbara," is currently living in Stockholm, but its statement made no mention of any request to Sweden for her extradition.
Velazquez, a Swedish citizen, faces up to life in prison if convicted.
Sweden has not received any requests to extradite the woman to the US, according to Per Claréus, press secretary to Justice Minister Beatrice Ask.
He told TT that if the US was to send an extradition request, it would be refused.