Former Gower AM Edwina Hart backed steel-coating firm Kancoat despite a warning of a "weak" business plan.
The Tories claim she may have broken the code because the firm was based near her constituency and she did not consult with the first minister.
The Welsh Government said the code was not broken.
Mrs Hart, who stood down from the assembly at the election in May, has been asked to comment.
Paragraph 4.4 of the Welsh Government's ministerial code, which sets out standards for their conduct, states: "Where ministers have to take decisions on their own portfolios which might have a particular impact on their own constituencies or electoral regions, they must take particular care to avoid any possible conflict of interest.
"Where ministers are uncertain about whether a conflict arises between their ministerial and constituency/regional responsibilities they should consult the first minister, for a decision as to how the business is to be handled."
A Freedom of Information request by the Welsh Conservatives found there was no record of any meeting between Mrs Hart and the first minister to discuss the granting of financial support to Kancoat.
Kancoat, which was based at the old Alcoa factory in Waunarlwydd, Swansea, was set up to coat metal used to make food cans and other products.
It was based less than half a mile outside Mrs Hart's Gower constituency.
Between May 2012 and February 2014 Kancoat was given a mix of loans and grants totalling £3.4m by the Welsh Government in decisions signed off by Mrs Hart.
The bulk of the support was given after the Welsh Government's own financial due-diligence reviewer raised concerns about Kancoat's financial projections in February 2013.
The review said Kancoat's business plan "appears weak and inconsistent" and the project was identified as high risk.
A request for support had previously been turned down by the government's investment arm Finance Wales due to an "unacceptably high" risk.
The company went into administration in September 2014.
A Wales Audit Office report in July revealed the company owed the government £2.6m - it created 12 jobs but ran into difficulties when it struggled to maintain its supply of steel.
Sir Alistair Graham, who chaired the UK's Committee on Standards in Public Life from 2004 to 2007, told BBC Wales he believed possible jobs for Ms Hart's constituents led to a potential conflict of interest.
Suzy Davies, Tory AM for South Wales West, said: "The decision comes off the back of a series of poor financial decisions made by the Welsh Government.
"I feel strongly that there needs to be an overhaul of the ministerial code, which in its current state lacks independence and transparency.
"It cannot be right that the first minister is the sole arbitrator of these rules."
Responding to the Conservative claims, a Welsh Government spokeswoman said: "The previous minister did not break the ministerial code."
The government had previously said the decision to support Kancoat was based on projections that more than 30 jobs would be created.
It has also pointed out that the factory was outside Mrs Hart's Gower constituency.
Asked in August whether Mrs Hart had broken the ministerial code, First Minister Carwyn Jones said: "No, she didn't.
"Where do you draw the line? For example if a decision is taken supporting a business in Cardiff, that business might employ people from many many different constituencies in reality.
"People don't work in the constituency where they live.
"The rule we have is you cannot take a decision on something that affects your own constituency, or is within your constituency.
"But the reality is nobody could take any decisions if we said you had to make sure that absolutely nobody from your constituency worked in a particular business before we offered it support.
"So that's the rule we keep and no, she didn't break the ministerial code."
Mr Jones said the former minister would not have needed to consult him about offering financial assistance to Kancoat "because the rule is you do not take a decision as a minister on something that has a direct effect on your own constituency within your own constituency".
A spokesperson for the Auditor General for Wales said his office is "considering the merits of conducting a broader-review into Welsh Government funding of businesses in Wales", which would include the funding of Kancoat.
An ex-economy minister has been accused by the Welsh Conservatives of breaking the ministerial code by approving £3.4m aid for a firm which later went bust.