The ground operation started after Turkish fighter jets and artillery bombed suspected PKK targets on Thursday, the military said on its website.
"After the successful bombing, a cross-border ground incursion backed by the air force started at 1900 (1700 GMT)" on Thursday, it said.
'Extraordinary response'
The Turkish army's general staff said in a statement: "The Turkish armed forces, which attach great importance to Iraq's territorial integrity and stability, will return home in the shortest time possible after its goals have been achieved."
Laurence Lee, Al Jazeera's correspondent in Istanbul, said: "I think Turkey sees a window of opportunity. It could it be that the Americans think the security situation in Iraq has stabilised very slightly and perhaps if there is fighting in the north it wont have any knock-on effects for the rest of the country.
"It could be that the Americans are now suddenly taking a longer term view and have decided that if they want to launch a military operation then they need Turkey to help them with that.
"But it is extraordinary that the only people that have come out against this is the Kurdish administration in northern Iraq and that everybody else seems to have suddenly accepted that it is ok to do."
On Friday, Mahmoud Othman, a member of parliament in the largely autonomous Kurdistan regional government, said that so far no armed conflict had been reported between the Turkish soldiers and the PKK.
'Possible invasion'
Speaking to Al Jazeera from Irbil, Othman said that Turkish newspapers had been reporting a possible invasion this spring, noting that the incursion into northern Iraq has been somewhat expected.
Hoshiyar Zebari, Iraq's Kurdish foreign minister, said: "Until this minute, we have not received anything from the border guards about Turkish forces crossing the international border."
Al Jazeera reported that four bridges had been hit in Thursday's air raid.
Recep Tayyip Erdogan, Turkey's prime minister, said: "I have spoken to Mr Bush (the US president) and informed him of the operation."
Reacting to the developments, a senior US official said on Friday that the Turkish land incursion was "not the greatest news".
Matthew Bryza, deputy assistant secretary of state, said: "A land operation is a whole new level."
Turkey regularly carries out air sorties into northern Iraq.
Byrza said Washington had been co-operating with Turkey in providing intelligence on PKK positions since last November to enable the Turkish air force to make pinpointed attacks - minimising civilian casualties.
'Limited duration'
Al Jazeera's correspondent Yousef al-Sharif said that Ankara had informed Baghdad and Washington of the incursion.
Al-Sharif said that the Turkish armed forces were planning to finish up their "integration operation" and return as soon as they can.
The US confirmed it was aware of the offensive, while the Iraqi government said it was not aware.
Rear-Admiral Gregory Smith, a US military spokesman in Baghdad, said the operation was understood to be of "limited duration" and specifically targeted Kurdish PKK fighters.
In a statement on Friday, he said: "Turkey has given its assurances that it will do everything possible to avoid collateral damage to innocent citizens or Kurdish infrastructure."