A journalist is reported to have died of a heart attack after being chased by protestors.
President Alfonso Portillo has ordered the army to restore order.
Mr Rios Montt - who ruled in the early 1980s, following a military coup - is appealing against a court ruling banning him from seeking the presidency in November's election.
Thousands of his supporters - some waving machetes and clubs - surrounded the United States embassy and the country's two highest courts on Thursday.
Demonstrators smashed windows, burned cars, blocked traffic and chased reporters covering the protest.
The violence prompted President Portillo to order soldiers onto the streets of Guatemala city.
"I will not permit any political movement to disrupt public order," Mr Portillo said.
Many of the protesters demonstrated outside the Supreme Court and Constitutional Court - which have both upheld a ban on his candidacy in November's election.
"From now on, we will not rest until the general is allowed to run for president," a protester said.
Controversial candidate
Mr Rios Montt, 77, was banned from standing in 1990 and 1995 because Guatemala's 1985 constitution bars former coup leaders from seeking the presidency.
A retired brigadier general, he took power in a military coup in March 1982 and was overthrown 18 months later.
He founded the Guatemalan Republican Front, which controls the presidency and dominates Congress.
Human rights groups say thousands of civilians died under his rule.
The US State Department has said it would be difficult for Washington to have a normal relationship with Guatemala if Mr Rios Montt was elected.
He now parliamentary speaker.