Led by dozens of protesters on motorcycles, the mostly youthful demonstrators filled city-centre streets in a rally organised by opposition parties and civil society groups.
Amid a heavy police presence, the marchers erected barricades of burning tires, and at least two buildings near the departmental police headquarters caught fire.
There were also clashes near the presidential palace, but no immediate reports of injuries.
"We demand that all those squandering (public) funds be tried and punished, their assets seized and turned over to the state for serious development projects, and that the president resign and turn himself in," said Velina Charlier, a protest leader.
The judges of the High Court of Auditors said in a voluminous report last week that Moise was at the centre of an "embezzlement scheme" that had siphoned off Venezuelan aid money intended for road repairs.
Venezuela's Petrocaribe aid programme has been plagued by allegations of corruption since its establishment in 2008.
The judges' report laid out a litany of examples of corruption and mismanagement.
The magistrates discovered, for example, that in 2014 Haitian authorities signed contracts with two different companies - Agritrans and Betexs - for the same road-repair project. The two turned out to have the same tax registration number and the same personnel.
Moise, before he came to power in 2017, headed Agritrans, which received more than 33 million gourdes ($700,000 at the time) to do the road work, though the company in principle did nothing but grow bananas.
The Petrocaribe scandal gave rise to parliamentary inquiries in 2016 and 2017, and public protests goaded the High Court of Auditors to examine how the $1.6 billion in Venezuelan funds were spent by succeeding Haitian administrations.
Opposition parties, who contested Moise's 2017 election, urged their supporters on Sunday to demonstrate peacefully.
At least seven Haitians died during violent protests in February that led to the fall of the government. But no new cabinet has been appointed, no budget has been approved, and there is no certainty when legislative elections will be held.
This comes amid a continuing economic crisis, with an inflation rate above 17 percent, the country's currency devalued, and many Haitians lacking basic necessities.