They would appear in court again on November 19, Colonel Sibongile Soci said.
The three face charges including arson. They were arrested on October 24 after a task team appointed by the Eastern Cape provincial commissioner investigated the incident.
The statue, which formed part of a heritage site, was burnt on October 22.
Tambo, born in Bizana, was among the founding members of the African National Congress Youth League in 1944 and became its first national secretary. He later became ANC president. Tambo died of a stroke in April 1993.