Mr Ban will visit refugee camps in the south where some 200,000 Syrians have taken refuge from the fighting across the border.
He will also hold talks in Ankara with Prime Minister Recep Tayyip Erdogan.
The visit comes as governments continue to warn Damascus not to use chemical weapons against rebel forces.
Mr Ban says that he has written to President Bashar al-Assad to warn that the use of such weapons would have “serious consequences”.
Speaking in the Iraqi capital Baghdad on Thursday, Mr Ban said President Assad should be “brought to justice” if his regime used chemical weapons.
“I have expressed my gravest concerns to (the) government of Syria and I have sent a letter directed to President Assad a couple of days ago,” Ban said.
“I have warned that in any case, if chemical weapons is used, then whoever (it) may be will have to be brought to justice, and it will create serious consequences to those people.”
The BBC’s James Reynolds in Turkey says it is not entirely clear what Syria’s actual capabilities and intentions may be.
Nato recently approved the deployment of Patriot anti-missile batteries along Turkey’s border with Syria.
The long-expected move came amid growing fears that Syria could use chemical weapons.
The Syrian government is believed to hold such weapons – including mustard gas and sarin, a highly toxic nerve agent – at dozens of sites around the country.
Damascus has never admitted having chemical weapons but said that, if it did, it would never use them against its own people.
One Western intelligence source has told the BBC that, so far, there has been no significant change in the movement or possible deployment of Syria’s chemical weapons stocks.
Washington has warned that the use of chemical weapons in Syria would represent a “red line” that could lead to greater US involvement in the conflict.
The BBC’s Middle East Editor Jeremy Bowen has just arrived in Damascus and says the situation there has deteriorated noticeably since his last visit in January.