The DfE has just published its accounts for 2014-15, nine months after every other government department.
The NAO says there is a level of "misstatement and uncertainty" that means the truth and fairness of the accounts cannot be verified.
The DfE says academies are subject to a "rigorous system of accountability".
While there is no suggestion that academies have misspent money, the NAO report warns that the rapid expansion of the academies programme in England has made it difficult to keep track of spending and land.
It also says the situation is likely to get worse given the government's drive to turn all schools in England into academies by 2020, or for them to have a plan to do so by 2022.
The report says: "The department's policy of autonomy for academies brings with it significant risks if the financial capability of the department and academies are not strengthened.
"And the financial statements do not present a true and fair view and meet the accountability requirements of Parliament.
"This will become even more significant in the context of the planned expansion of the academy sector."
The DfE is also criticised for not getting its accounts signed off in time.
The NAO says best practice means departments should aim to submit their accounts for scrutiny before the summer recess - a target all other departments met.
January is the official deadline, but the DfE  asked for an extension until 26 April.
The DfE said this was necessary because schools work on the basis of an academic year, while government departments operate according to the financial year.
Amyas Morse, head of the NAO, said: "Providing Parliament with a clear view of academy trusts' spending is a vital part of the Department for Education's work - yet it is failing to do this.
"As a result, I have today provided an adverse opinion on the truth and fairness of its financial statements.
"The department will have to work hard in the coming months if it is to present Parliament with a better picture of academy trusts' spending... in 2017."
An "adverse opinion" is the most serious view an auditor can give on a set of accounts and it is the second time the NAO has given this warning - the first being in January last year.
Since 2012, the DfE's group financial statements have also covered the financial statements of academy trusts, its executive agencies and non-departmental public bodies.
Included in this are 2,824 academy trusts that operated 4,900 academies between 2014 and 2015.
A department spokesman said: "Academies are subject to a rigorous system of accountability and oversight, tougher and more transparent than maintained schools.
"This is reflected in the NAO's finding that there are no material inaccuracies in individual academies' statements.
"However, the consolidation of thousands of those accounts into the format required by Parliament is one of the largest and most complex procedures of its kind.
"All of these accounts are published individually by trusts ensuring they can be held to account by the department and the public."
He said the department had developed a new methodology for the financial year 2016-17, which the NAO had said would provide a solution to a number of these issues.
He added: "With the Education Funding Agency's rigorous oversight of the academy system and the expanding role of the regional school commissioner, we are confident that the accountability system for the expanding academies programme is robust and fit for purpose."
Shadow education secretary Lucy Powell said: "This is a damning and very serious report, which highlights both the opaque financial arrangements within some academy chains as well as the almost impossible job the Department for Education has set itself in trying to directly run thousands of schools from Whitehall.
"Forcing all schools to become academies will make this situation even worse.
"If this report was about a local authority, it would rightly be put in special measures and taken over."
The Department for Education has been severely reprimanded by the National Audit Office for failing to properly account for spending by academies.