Blows were traded for several minutes but the fracas ended without serious injuries.
Vice President David Choquehuanca, who is also the president of Congress, announced that he would call the two political blocs for a meeting to try to ensure such scenes are never repeated.
Camacho, the conservative governor of the country's economic powerhouse region of Santa Cruz, was arrested on terrorism charges for his alleged role in the ouster of leftist president Evo Morales in 2019.
Morales stepped down after losing the support of the military amid strikes and protests in response to his disputed election to a fourth term.
Camacho's detention sparked countrywide protests.
He had come in third in presidential elections in October 2020 that were won by Arce, a Morales protege.
The charges against Camacho echoed the 2021 arrest of former president Jeanine Anez, who was given a 10-year prison term in June 2022 for allegedly plotting the toppling of Morales, her predecessor.
The alleged plot is dismissed as fictional by many, and Anez has consistently denounced what she calls political persecution.