The Grand Orange Lodge of Scotland has confirmed the politician had accepted an invite to the parade in Cowdenbeath, Fife, later this month.
A spokesman for the DUP said she would stress the need to build a shared society.
She is also planning to hold other meetings while in Scotland.
The spokesman said: “Mrs Foster has accepted an invitation from the Scottish Orange Order to speak at an event later this month.
“She will deliver the same message in Scotland as in Northern Ireland.”
At the event, Mrs Foster will say: “We need a United Kingdom where people feel at home and where they feel comfortable living and working regardless of their background.
“There is no place in 2018 for sectarianism or prejudice against any section of our community - that includes the Orange Order.”
She will also promote the idea of a United Kingdom “where people feel valued will endure”.
“People will be reluctant to leave the Union in such a circumstance.”
“Mrs Foster is planning to have other meetings when in Scotland,” a DUP spokesman added.
The Grand Orange Lodge of Scotland executive officer Robert McLean said he believed it was the first time she has attended one of the Boyne celebration parades in Scotland.
He said: “She’s been invited to be the guest speaker. The main speech would be by Arlene Foster.”
He added that attendance by Northern Ireland politicians at Scottish parades was not unusual and former First Minister and DUP leader Peter Robinson had done so in the past.
Ms Foster was Northern Ireland’s First Minister until the collapse of the powersharing agreement at Stormont last year.
The parade on 30 June is one of the biggest in Scotland and involves lodges from Fife, Edinburgh, the Lothians and elsewhere in Scotland’s central belt.
Labour and the Liberal Democrats in Scotland said Ms Foster’s time would be better spent in Northern Ireland, where there is no devolved government in place following its collapse more than a year ago.
Labour MP for Kirkcaldy and Cowdenbeath Lesley Laird said: “My advice to her would be to channel her energy into getting Stormont back up and running.”
Scottish Lib Dem leader Willie Rennie said: “With the Northern Ireland Assembly suspended, I would have thought that Arlene Foster’s time would be better spent reaching across the political divide at home rather than marching on the streets of a small town in Fife.”
Patrick Harvie, Scottish Greens’ co-convener, said: “If Arlene Foster does come across the Irish Sea she’d be better off discussing how to avoid a hard Brexit or learning about the importance of equal marriage or women’s access to free, safe and legal abortion, rather than taking part in yet another sectarian march.”