National Police spokesman Frantz Lerebours said the clash began when 20 to 30 people set fire to tires and fired weapons on an avenue on the outskirts of Port-au-Prince around 2 a.m. He said it wasn't clear if the victim was hit by police bullets.
Fourteen protesters were arrested, Lerebours said.
The remnants of burned tires were seen in at least three different neighborhoods in the Haitian capital later in the day.
"I woke up this morning and people were burning tires. I don't know why," said Roger Jean de Lance, 21, who lives in a tent camp near where the shooting occurred.
Some people said the protests might have been in reaction to an investigation by the Organization of American States into the results of the Nov. 28 election.
A year after a devastating earthquake, politically fragile Haiti has seen riots over allegations of fraud during the voting.
On Thursday, the OAS team of election experts presented its report to President Rene Preval. Although the report hasn't been made public, a draft obtained by The Associated Press recommended that Preval's preferred candidate be removed as one of the two candidates in the planned presidential runoff ballot.
Haiti's electoral council announced in December that government candidate Jude Celestin finished second just ahead of popular singer Michel Martelly by less than 1 percent of the vote, sparking rioting that shut down Haiti's capital for days. The OAS team said it concluded that Celestin came in third.
If that finding is followed, Martelly would compete with former first lady Mirlande Manigat in the second round. The runoff election was originally scheduled for Sunday, but put off because of disputes over the first round count.