He described it as a “stab in the back” committed by “accomplices of terrorists”.
Turkey says its jets shot at the plane after warning that it was violating Turkish airspace. But Moscow says it never strayed from Syrian airspace.
Nato is to hold an extraordinary meeting to discuss the incident at Turkey’s request.
Mr Putin warned there would be “serious consequences” for Moscow’s relations with Turkey.
Russian Foreign Minister Sergei Lavrov has said he was cancelling his visit to Turkey, where he was due on Wednesday, over the incident.
He also advised Russians not to visit Turkey and said the threat of terrorism there was no less than in Egypt, where a bomb attack brought down a Russian passenger plane last month.
He said the Su-24 was hit by an air-to-air missile fired by a Turkish F-16 while it was flying over Syrian territory.
President Putin said the plane had been attacked “at a height of 6,000 metres (20,000ft), 1km from the border”.
It crashed into Syrian territory 4km from the border, he added.
Analysis: Sarah Rainsford, BBC Moscow correspondent
This was tough language from an icy-looking President Putin. Much of his comments were for domestic consumption. After all, he launched air strikes in Syria arguing that it would make Russia safer; instead, 224 people were blown out of the sky last month in a bomb attack – and now this.
By rounding on Turkey, he is in part deflecting any suggestion that his own policy has backfired. But he is clearly furious too and it’s not clear yet how that will translate into action.
On state TV, there have been calls for a “tough response”; there’s talk of economic sanctions – and the foreign ministry has issued a travel warning, proclaiming Turkey as dangerous as Egypt following the terror attack on tourists there.
Since then, and the Paris attacks, there had been hints of a rapprochement between Russia and the West – uniting against a common threat. Ideally, Russia won’t want to scupper that, but this latest incident presents a huge challenge.
The two crew members ejected as their burning aircraft plunged into a Syrian hillside. Video footage has shown what appears to be the dead body of one of the flyers, surrounded by armed rebels.
“In any case, our pilots, planes did not threaten Turkish territory in any way. It is quite clear,” Mr Putin said.
“They were carrying out an operation against Isis [Islamic State] in the mountains of northern Latakia, where militants are focused – who mostly originate from the territory of Russia.
“So they were carrying the key task of preventative attacks against those who could return to Russia at any time. These are people who must be directly qualified as international terrorists.”
Turkish military officials said the plane was engaged after being warned that it was violating Turkish airspace.
It is the first time a Russian aircraft has crashed in Syria since Moscow launched air strikes against militants fighting Syrian President Bashar al-Assad in late September.
The Nato military alliance, to which Turkey belongs, said it was following the situation “closely” and was in contact with the Turkish authorities. There will be an “informational meeting” of ambassadors in Brussels at 16:00 GMT.
The UK-based Syrian Observatory for Human Rights said the jet had crashed in the mountainous Jabal Turkmen area of Latakia, where air strikes and fighting between rebels and Syrian government forces had been reported earlier on Tuesday.
Russian military helicopters searched for the pilot and navigator near the crash site in the predominantly Turkmen Bayir Bucak area, Turkey’s Dogan news agency reported.
A spokesman for a rebel group operating in the area, the 10th Brigade of the Coast, told the Associated Press that the jet’s crew had tried to parachute into government-held territory, but that they came under fire from members of the group.
One of them was dead when he landed on the ground, he added. The fate of the second was not immediately known.
Turkey, a vehement opponent of Syria’s president, has warned against violations of its airspace by Russian and Syrian aircraft.