The Turkish government has said its troops were responding - in line with their terms of engagement - to fire from members of the Popular Protection Units (YPG) as the militia advanced on the Syrian rebel-held town of Azaz, just 7km (4 miles) from the frontier.
But the international community is not convinced.
The US, France and EU have called on Turkey to hold fire, while the UN Security Council has urged it to "comply with international law".
Earlier this week, Turkish Prime Minister Ahmet Davutoglu said the shelling had succeeded in halting the YPG advance on Azaz and promised the "harshest reaction" if it tried to march on the town again.
"We will not allow Azaz to fall," he declared, adding that "the whole world should know this".
So why is this small town so significant for Turkey?
"Azaz and its surrounding area are very important for Turkey's national security and the future of the Syrian war," says Can Acun, a researcher from the Turkish pro-government think tank SETA.
"This area is on the land corridor stretching from the Turkish border to the city of Aleppo," he adds. "So both for humanitarian aid to go through and for the rebel forces to hold on to the area, Azaz is of strategic importance."
But this supply route to Aleppo was severed on 3 February as a result of a government offensive, backed by Russian air strikes, that broke a rebel siege of two towns south of Azaz.
Since then, the government advance northwards towards the border has continued, while the YPG has exploited the situation and begun pushing eastwards from their enclave around Afrin, taking the Menagh airbase and the town of Tal Rifaat from the rebels.
"The Azaz-Aleppo supply route does not function any longer," says journalist Cengiz Candar, who thinks the strategic importance of Azaz for the Turkish government is the result of other concerns.
"Turkey wants to portray this area to the US and the international coalition as somewhere they also can act against the Islamic State group. Furthermore, [if they capture it] the Kurds can join their enclaves along the border, which Turkey sees as a security threat," Mr Candar says.
Turkey views the YPG, the military wing of the Syrian Democratic Union Party (PYD), as allied to the outlawed Kurdistan Workers' Party (PKK), which has carried out a decades-long armed campaign in Turkish territory.
The PKK is listed as a terrorist organisation by Turkey, the EU and US. But Washington perceives the YPG and the PYD as the only effective force against IS on the ground in Syria.
Kurdish groups now control most of the Syrian border with Turkey, with only a 100km (62-mile) stretch remaining from Azaz to the IS-held town of Jarablus.
"Azaz is a symbol for Turkey," says Fabrice Balanche from the Washington Institute For Near East Policy.
"If the Kurds take Azaz, then they could join the land gap between their two enclaves, Kobane and Afrin. Prime Minister Davutoglu fears that if the Kurds capture Azaz, they could start a big offensive from Kobane to the west and from Afrin to the east," he explains.
But Cengiz Candar believes the YPG could join the enclaves without taking control of Azaz.
The demographic structure of Azaz is of importance to Turkey as well, since along with Arabs and Kurds, ethnic Turkmens live in the area too.
"Azaz is also of key significance because of the support provided for rebel groups from within Turkey," says Fabrice Balanche.
"If the Kurds capture Azaz, the rebel groups will not have an entry point into Syria. That's Russia's strategy. Very simple - let the Kurds take control of the border area and cut Turkey from Aleppo."
On Tuesday, the pro-government Turkish newspaper Sabah reported that about 500 rebels from Idlib province had travelled via Turkey to Azaz in the past few days.
So would Turkey risk getting involved unilaterally in the Syrian war, for the sake of protecting Azaz?
Turkish Defence Minister Ismet Yilmaz recently made it clear that there were no plans to send ground troops into Syria.
A Turkish official speaking to the BBC also reiterated that Turkey did not intend to act unilaterally unless there were major changes on the ground, but that it was trying to convince the US-led coalition against IS to send troops in.
"I think if Turkey and the Gulf countries are seriously determined, they can convince the US to change its position," says Can Acun.
"Such a step could provide a safe zone for [displaced Syrians] too, and could well get the support of the EU which has been facing an overwhelming refugee crisis," he says.
However, Fabrice Balanche thinks Washington is not interested in getting dragged further into the Syrian conflict, and that the proxy war would continue instead.
"The US wants to keep the Kurds by its side. But Washington knows if Ankara continues with the shelling, then the Kurds will shift towards Russia," he says. "So the US needs to negotiate between Turkey and the Kurds. But it's difficult because the US is weak at the moment - it's the election year."
"The Turks will probably wait until next year for a new US administration that would get more involved in Syria and more aggressive with Russia. Probably, they are dreaming of a new Ronald Reagan who says: 'America is back'," Mr Balanche says.
Turkey is facing mounting criticism for shelling Kurdish forces across the border in northern Syria.