In a ruling, European ombudsman Emily O'Reilly was critical of the EEAS and also said the EU should start paying all its trainees at delegations abroad.
The Irish-born official judged that the practice of unpaid internships by the EEAS "unfairly favoured a privileged few."
Her comments come after she investigated a complaint by an Austrian EEAS trainee who had filed a complaint about the organisation's unpaid internships.
In the ombudsman's view, "unpaid traineeships may lead to a discriminatory situation since persons from less privileged backgrounds are likely to lack the financial means to undertake a traineeship."
The Strasbourg-based official said, "They will thus miss out on this valuable opportunity to enhance their qualifications and skills. Moreover, the practice of having unpaid trainees may be counterproductive in identifying the best suited candidates."
The ombudsman said the EEAS employed some 800 unpaid trainees at its delegations worldwide.
The EEAS reportedly had a staff of 4189 at the end of 2015, with 2261 in its various delegations in 139 countries.
On Monday, however, an EU spokesperson countered the criticism, telling this website action had been taken by the EEAS to tackle the issue.
The spokesperson said, "As noted by the ombudsman's assessment, the EEAS has taken steps to address several of the issues raised in the investigation, in particular concerning information on traineeships for candidates.
"Therefore, the EEAS is already offering more transparency about the traineeship opportunities and about the procedure for applying for traineeships through its website and it has issued guidelines for traineeships in delegations providing more clarity on traineeship conditions."
Regarding the financial aspect that was raised by the ombudsman, the spokesman said the EEAS "will now assess and review the scheme for unpaid traineeships in delegations, including its budgetary dimension.
"The EEAS also offers opportunities for remunerated traineeships on a regular basis, both in its headquarters and in delegations through the Blue Book scheme and through the programme for young experts in delegations."
The ombudsman's recommendations are non-binding, but EU institutions usually follow them. The EEAS has until 31 May to submit a formal answer.
Elsewhere, the European Parliament has banned unpaid internships in its secretariat, but MEPs are still free to propose such internships in their offices. The European Commission offers 200 unpaid internships at any one time.