Flight 951 was attempting to land at a Port-au-Prince airport when it was struck by gunfire, the Haiti National Office of Civil Aviation told ABC News.
The flight was diverted and landed safely in Santiago, Dominican Republic.
The airline said one flight attendant was being checked by medical crews due to minor injuries.
No other passengers reported any injuries.
Spirit Airlines said the plane was taken out of service.
All of the airline's services at Toussaint Louverture International Airport in Port-au-Prince and Cap-Haitien (CAP) were suspended.
The U.S. Embassy in Port-au-Prince said the "security situation in Haiti is unpredictable and dangerous."
The U.S. Embassy added the following statement:
"The U.S. government cannot guarantee your safety traveling to airports, borders, or during any onward travel. You should consider your personal security situation before traveling anywhere in Haiti. Only attempt to depart Haiti or travel within Haiti if you believe it is safe for you to do so."
American Airlines and Jetblue said they suspended services to Haiti until Thursday, Nov. 14.