Refugees and migrants seen heading to the borders reportedly include Syrians, Iranians, Iraqis, Pakistanis, Afghans and Moroccans.
Turkey has opened its borders with Europe, allowing Syrian refugees and other migrants to pass through, an official has said.
It follows the killing of 33 Turkish soldiers by Russian-backed Syrian government troops.
It is the deadliest attack suffered by the Turkish army in almost 30 years - the assault in Idlib marking a serious escalation in the conflict.
"We have decided, effectively immediately, not to stop Syrian refugees from reaching Europe by land or sea," a senior Turkish official told the Reuters news agency.
"All refugees, including Syrians, are now welcome to cross into the European Union."
It means Ankara has effectively stopped abiding by a deal struck with the EU in 2016 to stop refugees reaching Europe.
Within hours, dozens of migrants were seen heading towards the European frontier.
"We heard about it on the television," said Afghan migrant Sahin Nebizade, 16, who was among a group packed into three taxis.
They had come from Istanbul and were heading for a border crossing to Greece.
Greece and Bulgaria said they would reinforce their frontiers immediately. Greece sent more police to its northern border and increased maritime patrols around its islands.
At a land crossing between Pazarkule in Turkey and Kastanies in northeastern Greece, police buses were seen denying access to hundreds of people.
"They will not enter the country. They are irregular migrants - we won't let them enter," a Greek government official said.
Greek Prime Minister Kyriakos Mitsotakis tweeted: "I want to be clear: no illegal entries into Greece will be tolerated. We are increasing our border security."
Demiroren news agency broadcast drone footage on Friday showing around 300 migrants, including women and children, walking through northwest Turkey.
It said the group included Syrians, Iranians, Iraqis, Pakistanis and Moroccans.
Sky's Mark Stone said Thursday night's airstrike demonstrates "how convoluted and conflicted this Syrian conflict has become".
As a consequence, Ankara has struck back, triggering the potential of a much larger conflict between the Syrian regime and Turkey.
Turkish president Recep Tayyip Erdogan has now spoken with his Russian counterpart Vladimir Putin - with both agreeing to meet as soon as possible.
NATO members are deeply divided over Turkey's actions in Syria, and European allies are worried about any new wave of refugees arriving.
Stone said: "The Turks have wanted for some time for NATO to get involved. They would like a no-fly zone put over northwestern Syria, they say, to protect the civilians."
Nearly a million of them have moved up to the northwestern corner of Syria to try and escape the fighting in and around the city of Idlib.
Sky News gained rare access to northwest Syria, where special correspondent Alex Crawford found indiscriminate bombing of civilian targets, thousands of displaced people fleeing violence and what she described as "obvious war crimes".
Stone said: "Turkey clearly has ulterior motives for wanting a NATO no-fly zone - they want to protect those northeastern and northwestern parts of Syria for their own political reasons."
There are 3.5 million Syrian refugees in Turkey.
Since the 2016 deal with the EU, President Erdogan has repeatedly threatened to "open the gates" in several disputes with European states.
Stone said Mr Erdogan has the ability to "switch the tap on and off" in terms of allowing refugees into Europe, adding "there are this morning images similar to those we saw in 2015 of refugees crossing the border".
He said: "(There are) much, much smaller numbers but what I think Turkey is trying to do is put huge pressure on NATO, who are meeting this morning in Brussels to discuss it."
It comes a day after Omer Celik, a spokesman for President Erdogan's ruling party AKP, said NATO should stand by Turkey's side.
In a message seemingly aimed at Europe, he added: "Our refugee policy is the same but there's a situation there, we're no longer able to hold refugees."