Haitian Foreign Minister Claude Joseph tweeted that he had phoned his Turkish counterpart Mevlut Cavusoglu to thank him for arresting "one of the people of greatest interest to the investigation" into Moise's death.
Moise was shot on 7 July at his home in Port-au-Prince and while dozens of people have been arrested, the identity of those who ordered the attack remains a mystery.
Last month, a former Colombian military officer wanted by Haitian authorities over the assassination was captured in Jamaica.
Three Colombians were killed by Haitian armed forces responding to the attack and 18 more were detained, alongside two US citizens of Haitian descent.
The assassination deepened an already dramatic crisis in Haiti, which is suffering from a lack of security, soaring gang violence and a spate of kidnappings.