French Defense Minister Jean-Yves Le Drian confirmed that the twin-prop Fairchild Metroliner went down near the runway of the southern Mediterranean island nation's main airport on Monday morning.
"A light reconnaissance aircraft ... carrying out surveillance operations over the Mediterranean for the defense ministry crashed this morning at 0630 at Malta's Luqa airport, during take-off," the defense minister said.
The minister noted that three of the victims were ministry staff while the other two were contractors.
The French daily Le Monde reported that the officials belonged to France's intelligence services.
Video footage showed flames and thick black smoke billowing from the site of the crash, next to the runway.
The Maltese government said in a statement that inquiries were under way to determine what had caused the crash. "Official information, footage and eyewitnesses ... clearly indicate that there was no explosion prior to impact."
The officials have not yet ruled out sabotage as a possible cause of the crash.
Airport officials said the plane had been heading for the city of Misrata in Libya, where some countries have sent teams of special forces to support the new UN-backed Government of National Accord (GNA) in its ongoing fight against the Takfiri Daesh militant group.
Malta's government said that the flight had been due to return to Malta within hours without landing in any other countries.
On July 20, French Defense Ministry confirmed the death of three of its soldiers who it said were on a mission in Libya. The French soldiers were killed in a helicopter crash in Magrun, south of the Libyan coastal city of Benghazi.
France had previously said its planes were involved in reconnaissance flights in areas controlled by Daesh militants in Libya but it was the first time it was confirming the presence of special forces on the ground in the country.
Libya has been the scene of violence since 2011, when an uprising coupled with NATO military intervention led to the toppling and killing of longtime dictator Muammar Gaddafi.
Daesh, which is mainly active in Syria and Iraq, has taken advantage of the political chaos in Libya to increase its presence there.