Photos showed Ms Mogherini surrounded by a number of male MPs, taking photos.
Many social media users criticised the MPs, ridiculing them or labelling their actions "humiliating".
The Fars news agency posted a photo which many social media users felt showed Ms Mogherini unimpressed - and labelled the MPs' behaviour "strange".
One MP, Alireza Salimi, called the behaviour "self-surrender to the West", and said that a committee on the conduct of members may probe the incident - if other MPs complain that the selfies caused "contempt" for parliament.
The EU has issued a number of sanctions against Iran over human rights and the country's nuclear programme.
But while Mr Salimi felt the behaviour signalled subservience towards a top Western official, many on social media ridiculed the image of men crowding Ms Mogherini.
One popular tweet compared the image to a scene from the film Malena, where crowds of men rush to light actress Monica Belluci's cigarette.
Another made the same point using of an iconic image from Walt Disney's Snow White and the Seven Dwarves.
Ahmad Mazani, one of the MPs in the controversial pictures, tweeted that lawmakers had been banned "from interacting with special guests" during the ceremony - explaining the rush to crowd Ms Mogherini at its conclusion.
But Twitter users remained critical, with one replying that the MPs had "embarrassed the nation".
Hesam Ashena, the cultural adviser to the president, said: "This is a cultural rather than a political problem. Every one of those esteemed MPs in that selfie should be interviewed seriously."
Sadegh Kharrazi, an adviser to reformist former President Mohammad Khatami, suggested that all Iranian MPs undergo "a training course on codes of conduct and universal moral values".
Ms Mogherini - who has built closer ties between the EU and Iran since her appointment - released a statement about the visit to Iran, but made no comment about the related controversy.
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