The incident happened in the area of the Kasab crossing, which has been the scene of fighting between rebels and Syrian regime forces.
"A Syrian plane violated our airspace," Mr Erdogan told an election rally of his supporters in north-west Turkey.
"Our F-16s took off and hit this plane. Why? Because if you violate my airspace, our slap after this will be hard."
The rebels had been fighting for control of the Kasab crossing since Friday, when they launched an offensive Syrian authorities said was backed by Turkey's military.
Syria has responded to the incident by accusing its northern neighbour of "flagrant aggression".
It said Turkish air defences shot down the MIG-23 jet while it was attacking rebel forces inside Syrian territory.
Syrian state media quoted a military source as saying the pilot managed to eject from the plane.
The Turkish military said two Syrian MIG-23 planes approaching its airspace were warned "four times" to turn away and it scrambled fighter jets when one refused to do so.
In a statement, Turkey said the plane breached its airspace by about 1 kilometre and flew over the country for another 1.5 kilometres.
"One of the patrolling F-16 jets fired a missile at the Syrian plane ... in line with rules of engagement, and the plane fell into the Kasab region on Syrian territory," it said.
'Turkey's determination should not be tested': defence minister
Turkish president Abdullah Gul congratulated the country's armed forces following the incident and defence minister Ismet Yilmaz said Turkey had the "strength" and "capacity" to protect its borders.
"Turkey's determination should not be tested," Mr Yilmaz said.
The pro-opposition Syrian Observatory for Human Rights monitoring group said initial reports from the area said the plane came down on the Syrian side of the border.
Most border fighting between Syria and Turkey has been further north and to the east of the incident site.
Al Manar, the television station of the Syrian regime's Lebanese ally Hezbollah, said two rockets had been fired from Turkish territory at the Syrian jet.
After the Syrian air force downed a Turkish fighter jet in June 2012, Turkey toughened its rules of engagement to say any military approach of its border from Syria would be considered a threat.
Turkish warplanes last year downed a Syrian helicopter, which Ankara said was detected 2 kilometres inside Turkish airspace.
A staunch opponent of the regime in Damascus, Turkey hosts more than 750,000 refugees from the three-year Syrian conflict, many of them in camps along the border.