The march itself, which was attended by thousands, was peaceful, police said.
Four journalists were injured when protesters threw stones and petrol bombs at police after the march.
The run-up to the 11 September anniversary of the 1973 coup, when Gen Augusto Pinochet overthrew Salvador Allende, is often marked by violence.
In 2012, one police officer died during clashes.
On Sunday, thousands of Chileans marched through the streets of the capital, Santiago, to the memorial to the disappeared.
They were carrying banners with the names and pictures of people who disappeared under Chile's military rule.
According to official figures, 40,000 people were victims of human rights abuses under the dictatorship and more than 3,000 were killed or disappeared.
Police said a small group of hooded protesters threw stones and sticks at police after the march had reached the cemetery where the memorial to the disappeared is located.
Government spokesman Alvaro Elizalde said those who had been involved in the violence would be charged.
"These are serious offenses, which we strongly condemn and which can't go unpunished."
A journalist from Chilevision was hurt when he was hit by a molotov cocktail in the head, another journalist and two cameramen were also injured.
Mr Elizalde stressed that those causing trouble were part of a "very small group".
He said police would be out in force on 11 September, when more marches are planned.

A drilled shot by experienced Slovenia international Milivoje Novakovic threatened to leave Aberdeen with an uphill task in next week's return leg.
But Republic of Ireland international Hayes finally converted one of the many chances the Dons created at Pittodrie.
However, Aberdeen will need to score in Slovenia to stay in the tie.
All seven of the Dons' goals in the previous two rounds had come in the last 22 minutes of matches, with three in stoppage time.
And though there was a constant threat from Derek McInnes' side, full of pace, movement and intensity, they could not find a way past goalkeeper Jasmin Handanovic until the closing stages.
The aim from McInnes was to disrupt a team who like to slot into a steady defensive pattern in an effort to get an early goal.
Top scorer Adam Rooney fastened on to a mistake by Dare Vrsic, but the striker's shot was indecisive and Handanovic saved at the second attempt.
The visitors then squandered the best early chance after a great run and cross on the counter-attack by right-back Denis Sme, Marwan Kabha sending his shot from 12 yards hopelessly over the bar when he should have scored.
Handanovic made a brave block at Rooney's feet and then saw the same player miss an excellent Andrew Considine delivery by inches as crosses kept flashing across his penalty box.
The keeper again excelled by blocking Jayden Stockley's header at point-blank range just before the break.
Vrsic caused a few moments of anxiety for Aberdeen when stopper Joe Lewis was forced to make a sharp dive to his left to prevent the former Austria Vienna player netting.
Rooney did have the ball in the net after some great build-up play by Niall McGinn but the striker had strayed offside. Then, with time running out, Novakovic struck.
It was a wonderful finish from the 37-year-old as he brushed off the challenge of Ash Taylor before arrowing a shot beyond the despairing dive of Lewis.
But Taylor redeemed himself with a determined contribution to set up Hayes' sidefoot finish minutes later.
That gives Aberdeen greater hope of reaching the play-off round, but Maribor know they will progress if they avoid losing a goal next week.
Police and protesters have clashed in Chile's capital following a march to remember those who disappeared under military rule from 1973 to 1990.
[NEXT_CONCEPT]
Aberdeen struck late in Europe again as Jonny Hayes equalised against Maribor in the Europa League third qualifying round first leg.