The regulator said it had concluded that contents of the report, called Plan A+ Creating a Prosperous Post-Brexit UK, and an associated launch event "amounted to misconduct and mismanagement" by the charity’s trustees.
The commission said the report, which was removed by the charity from its website last year, was insufficiently balanced and neutral.
"Specifically, the commission finds that the report and its launch sought explicitly to change government policy on an issue unrelated to the charity’s purposes – furthering education – which constitutes a breach of the commission’s guidance on political activity and campaigning," the regulator said in a statement.
The charity’s launch event for the report included only speakers "who held a particular set of views", which risked "the public perception that the IEA is politically biased and has a political viewpoint on a key government policy", the commission said.
The commission added that furthering education did not need to be "value-free or completely neutral", but research reports must present balanced information.
"In this case, the commission found that the report was not sufficiently balanced and neutral, and nor did the charity provide an equally prominent publication or event presenting a different view, which could have provided balance in the round," the commission said.
The warning says the charity’s trustees must provide the regulator with written assurances that it will not engage in campaigning or political activity that contravenes legal or regulatory requirements.
If the charity does not comply with the warning, the regulator can take more serious action, such as suspending trustees or appointing an interim manager.
The IEA remains the subject of an ongoing regulatory compliance case, which is examining concerns about trustees’ management and oversight of the charity’s activities.
The charity said last summer that it made no apology for seeking to raise funds after claims were made that it offered ministerial access to potential US donors.
David Holdsworth, deputy chief executive of the Charity Commission, said: "Most charitable think tanks understand the rules that are associated with charitable status and are careful to ensure their work complies with our guidance and inspires public trust.
"I hope that our official warning now encourages the trustees of the IEA to recognise and understand that they must run the organisation as a charity and comply with charity law."
Neil Record, chair of the IEA, said the charity was "considering a range of options" because it felt the warning had "extremely widespread and worrying implications for the whole of the think tank and educational charity sector".
He said: "A precedent is being set: research papers – and their launches – that put forward policy proposals might now fall outside the parameters of what the Charity Commission considers acceptable activity."
He said the charity would be working with the regulator to address those points.