The US and other delegations left early after shooting rang out as the event got under way.
Protesters blamed some of those at the service for the leader's death.
Authorities accuse foreign mercenaries of the killing but questions about the attack remain.
The president's widow Martine, who was injured in the attack and treated in hospital in the US, was at the funeral with three of her children.
"Cry for justice. We don't want revenge, we want justice," she said, according to Reuters news agency.
The president's coffin was carried by men in military uniform. It sat on a stage in a Haitian flag, surrounded by white flowers. A Roman Catholic priest blessed it.
But even the funeral could not escape the unrest suffered by Haiti for so long.
Protesters clashed with police outside the venue and witnesses smelt tear gas at the ceremony, but it seems nobody was hurt.
Some officials faced the anger of demonstrators, with police chief Leon Charles accused of being an "assassin".
Haitian police accuse a group made up of 26 Colombians and two Haitian Americans of carrying out the killing. At least 20 were detained, while three were killed by police and five are still on the run.
Moïse, 53, had been president of Haiti, the poorest nation in the Americas, since 2017. His time in office was rocky as he faced accusations of corruption and there were widespread demonstrations against him earlier this year.
Also this week, a new prime minister, Ariel Henry, was sworn in after a political row with a rival.
He has called for unity and said he would form a temporary government until elections, due in September.