His death has left Haiti in an even deeper constitutional and political crisis as it has only a handful of elected officials nationwide.
Mr Henry, a political moderate and neurosurgeon whom President Moise named prime minister just days before his death in an attempt to reduce political tensions, has sought to forge a new consensus between different political factions.
But allegations over his possible involvement in President Moise's killing are now overshadowing that.
Mr Bed-Ford Claude said last week that phone records showed Mr Henry had twice communicated with a man believed to be the mastermind behind President Moise's killing on the night of the crime.
That suspect, a former justice ministry official whom Henry has publicly defended, is now on the run.
Mr Henry dismissed his request to discuss the matter as politicking and did not respond to the allegations.
That prompted Prosecutor Claude to write on Tuesday to the judge overseeing the investigation into President Moise's slaying and ask him to charge Mr Henry as a suspect.
He also wrote to Haitian migration services ordering them not to let the prime minister leave the country "due to serious presumption relative to the assassination of the president".
Seeking political stability
Decades of political instability as well as natural catastrophes have plagued Haiti's development. Its aid-dependent economy is the poorest in the Americas, more than a third of Haitians face acute food insecurity, and gangs have turned swathes of the capital into no go areas.
Mr Claude had invited Mr Henry on Friday to meet with him to discuss the phone calls with the suspect, noting that he could only summon the premier on presidential orders, but that the country remained without a president.
Haiti's Office of Citizen Protection demanded on Saturday Mr Henry step down and hand himself over to the justice system.
Mr Henry retorted on Twitter that "no distraction, invitation, summons, manoeuvre, menace or rearguard action" would distract him from his work.
The prime minister announced on Saturday that Haiti's main political forces had reached an agreement to establish a transition government until the holding of presidential elections and a referendum on whether to adopt a new constitution next year.
The agreement establishes a Council of Ministers under Mr Henry's leadership. A constituent assembly made of 33 members appointed by institutions and civil society organisations will have three months to prepare the new constitution.
Mr Moise's own attempts at holding elections and a constitutional referendum were attacked for being too partisan. Critics called them veiled attempts at installing a dictatorship.
His supporters said he was being punished for going after a corrupt ruling elite and seeking to end undue privileges.