Colombia's Attorney General Eduardo Montealegre said the office was run by a criminal organisation that had intercepted emails from a Farc rebel negotiator and the government.
He said President Juan Manuel Santos was also "probably" targeted.
Peace talks began in Cuba in 2012 to try to end five decades of conflict.
"This office intercepted emails from the press chief of the Farc in (the Cuban capital) Havana, an institutional email from the national government, and two emails from Cuban journalists who are covering the peace process in Havana," Mr Montealegre told a news conference in Bogota.
"The purpose of this office, the purpose of the people who were involved in this criminal enterprise, was to sabotage, interfere and affect the peace process in Havana," he said.
"It appears that, through this office of interceptions, the emails of the president of the republic were also probably intercepted."
One person, Andres Sepulveda, was arrested for allegedly running the operation and selling the information he obtained to third parties.
The attorney general said they were investigating who was paying to gain access to the information.
The Farc, Colombia's largest guerrilla group, has been in talks with the government in Cuba since November 2012 to try to end the longest-running internal conflict in Latin America.
Hundreds of thousands of people have been killed and some three million more have been internally displaced since the two sides began fighting in the 1960s.
President Santos has said he hopes to sign a peace treaty with left-wing rebels this year.
Colombian authorities say they have raided an office that illegally spied on rebel and government communication to try to undermine peace talks.