The funds are on top of the £11 billion-plus block grant allocated under the Barnett model for devolved regions.
Northern Ireland Secretary Karen Bradley said on Thursday the money recognises the lack of opportunity for “fundamental service reconfiguration” in the current financial year.
The SNP has demanded to know when Scotland will receive a comparable share of extra cash, saying an equivalent share for the country - which has a larger population than Northern Ireland - would be £400 million.
The party has accused the Conservative Government of “delivering a grubby Brexit bung to buy off DUP votes” ahead of crucial votes on Brexit this month.
UK ministers have insisted the £140 million is to address specific challenges in Northern Ireland.
SNP economy spokeswoman Kirsty Blackman has written to Scottish Secretary David Mundell, asking various questions about the funding.
The letter asks him: “Why do you support additional money for Northern Ireland but not a proportionate increase in funding for Scotland?”
Commenting later, Ms Blackman, the MP for Aberdeen North, said: “The Tories are delivering another bung for the DUP, ripping up the rule book in the process.
“But if the rules are to be applied as they should be, then Scotland’s fair share would amount to an extra £400 million for public services here.
this additional funding will not result in Barnett consequentials for Scotland. To suggest it should is to fail to understand how the Barnett formula works.”
“This problem lies at the door of David Mundell, who has disgracefully failed to fight Scotland’s corner right the way through the Brexit process.
“This extra cash for Northern Ireland comes just before Theresa May brings her bad Brexit deal back to Parliament - where every MP’s vote will count.
“And it is crystal clear that the Tories are delivering a grubby Brexit bung to buy off DUP votes whilst Scotland’s voice in the Brexit process is ignored.”
A UK Government spokeswoman said: “Like previous Northern Ireland support packages, or funding for city and growth deals in Scotland, the £140 million funding addresses specific challenges.
“As there has been no increase in spending on devolved matters in England, this additional funding will not result in Barnett consequentials for Scotland. To suggest it should is to fail to understand how the Barnett formula works.”