The Scottish Government says figures quoted by the Treasury in a presentation on the financial implications of a Yes vote are based on "blatantly flawed and false information".
Mr Swinney has written to the department's Permanent Secretary Sir Nicholas Macpherson calling for an "urgent investigation".
His complaint comes ahead of the publication of the Treasury's latest analysis on the costs of independence from 2016 to 2035/36.
The Institute for Government and the London School of Economics have published analysis which puts the average cost of setting up a new policy department at £15million.
Applying this to "the 180 departments the Scottish government states it would need" would cost £2.7billion, the Treasury said.
The figures, Mr Swinney said, are "patently untrue".
In his letter to Sir Nicholas, Mr Swinney wrote: "It is essential that the public can make a balanced judgment on the referendum debate.
"The misinformation presented in this publication places serious doubts over the accuracy of the full Treasury analysis expected later this week and previous Treasury works on Scotland becoming independent."
Mr Swinney added: "The Scottish Government has no intention of creating 180 government departments or even 180 public bodies.
"There is no mention of this in the Scottish Govern-ment's white paper.
"I would appreciate urgent clarity from yourself as to whether this material was approved by you and on what basis and an explanation of how such blatantly false figures came to be presented to the media."
A UK Government source said: "This is an own goal by the Scottish Government. Their own white paper says an independent Scotland will need 180 public bodies."