The motive was not immediately clear but officials said they believed the shooter had acted alone and described the attack as a “criminal act”.
It followed a similar shooting on Sunday in the nearby city of Toulouse when an off-duty soldier was shot dead by an assailant on a motorcycle.
The defence ministry said the three soldiers, from the locally based 17th Parachute Engineering Regiment (RGP), were aged 28, 26 and 24.
After initially announcing the death of the 28-year-old, the ministry retracted the statement and said he had been airlifted to Toulouse for treatment. His life was in danger, the ministry said.
Police said the two others died on the spot.
“All avenues and motives of a very different nature must be considered, from an individual act to something that was collective and organised. We don’t know,” Defence Minister Gerard Longuet told reporters after arriving at the base.
Asked if he thought the attack targeted the military itself, Longuet said: “I don’t think so, I hope not… But for the moment there is nothing that rules out this or that theory.”
Local officials said the shooting took place around 2.10 pm (1310 GMT) on a street not far from the base housing the regiment, which has recently served in Afghanistan.
Officials said the gunman, wearing a helmet with visor, got down from the scooter, fired on the three uniformed soldiers on a street near shops and a bank branch, then got back on and drove off at speed.
Investigators found 15 spent cartridges at the scene, police said.
The official told AFP it was not clear if the victims were withdrawing money from the bank, but a television news report of the incident said that one of them had.
Authorities launched an extensive search for the gunman involving a large number of police and national gendarmes, the official said.
In Sunday’s incident, a 30-year-old soldier was shot dead by an assailant on a motorcycle in a residential area of Toulouse, 45 kilometres (30 miles) south of Montauban.
Prosecutors said they were considering a number of possibilities in that shooting, including that it was the result of a personal dispute.
Toulouse prosecutor Michel Valet said they were asking “serious questions” about the similarities between the two incidents.
President Nicolas Sarkozy was cautious in reacting to the incident.
“The circumstances are confusing and at this time we cannot give any kind of explanation,” he told reporters. “It is a murder, that is undeniable, but we cannot say what the motives were.”
Thursday’s victims were from a 1,000-strong unit of sappers specialised in mine and explosives clearance, breaching fortifications and urban warfare.
In recent years the 17th RGP has often been deployed on operations in Afghanistan, Lebanon and the Balkans. It was founded in 1946 and fought in colonial wars in South East Asia and participated in UN missions in Korea.
It is headquartered in Montauban in a region which is home to all of France’s elite airborne units.
France still has more than 3,000 soldiers deployed in Afghanistan as part of the NATO-led mission fighting the Taliban.
Montauban deputy mayor Brigitte Bareges said the community was “shocked and appalled” by the shooting.
She offered her condolences to the families of the soldiers, noting that the regiment “has already paid a heavy price in the war in Afghanistan with four soldiers dead for France”.