Navy officials identified the crew members as U.S. Coast Guard Ensign Morgan Garrett, 24 years old from Weddington, North Carolina and U.S. Navy Lt. Rhiannon Ross, 30 years old from Wixom, Michigan.
Ross was an instructor pilot, the Navy statement said, while Garrett was identified as a student aviator.
The crash occurred southeast of Mobile, near the city of Foley and the town of Magnolia Springs. Darby called the neighborhood a "heavily populated" residential area. No firefighters were injured, he added.
The plane had flown out of Naval Air Station Whiting Field, about 30 miles northeast of Pensacola, Florida, Navy spokeswoman Julie Ziegenhorn said.
The U.S. Department of Defense and the Navy were set to handle the investigation, the Baldwin County Sheriff's Office tweeted.
The Associated Press contributed to this report.