"There are sufficient compromising elements that form (my) conviction on the appropriateness of prosecuting Mr. Henry and requesting his outright indictment," Claude wrote to the court, according to Agence France-Presse.
Henry represents a flight risk and thus should be "forbidden from leaving the national territory by air, sea or road due to serious presumption relative to the assassination of the president," the prosecutor wrote in a letter to Haiti's Migration Services.
Moïse was assassinated July 7 in what was called a "highly coordinated" attack on his residence, the country’s acting prime minister confirmed in a statement then.
Phone records show suspect Joseph Badio called Henry twice in the hours after the 1 a.m. killing, according to the prosecutor.
Those calls were made at 4:03 a.m. and 4:20 a.m. by Badio not far from the scene of the crime, Claude added.
The telephone calls lasted for a total of seven minutes as Henry was staying at the Hotel Montana in Port-au-Prince at that time, according to Claude's court document.
A representative for Henry declined immediate comment.
Before the deadly attack, Moïse had tapped Henry to be the next prime minister in a move widely seen as a bid to calm the opposition.
But the move later backfired because the main opposition coalition said Moïse did not consult with them before picking Henry.
The opposition did not recognize Moïse as president by the time he was killed. Recently, opponents have gone as far as calling Henry a puppet of the international community.