The attack took place during the meeting of the Internet Governance Forum in Baku, the Azerbaijani capital.
It came as Kroes finalises a new cyber security policy paper which the European Commission aims to publish next month.
Kroes spokesman Ryan Heath said the attack occurred while they were in their hotel.
Heath said he and a colleague received computer messages warning them that their computers had been accessed by an unknown device, something he said he believed was an attempt to spy on him.
The attack was made on a personal computer “that had only my photos and Kroes’ statements on it, since the hard drive was recently wiped clear for a repair,” Heath said.
'Problems with free expression'
Kroes used the incident to lambaste the Azerbaijani government for its lack of privacy and press freedoms in a blog entry on 10 November, citing the hacking as one of several violations which she said highlighted the "harsh" reality of political life in Azerbaijan.
“We mentioned it because it served to underline our point about problems with free expression in Azerbaijan, rather than because of any obvious damage done,” Heath told EurActiv, adding that the computer was being analysed to check if what if anything was copied from it. “No Commission device was compromised,” he added.
Kroes said in her blog: “Activists were harassed at the internet conference. My advisors had their computers hacked. So much for openness. The reality in Azerbaijan is harsh. We see many arbitrary restrictions on the media. We see the exercise of free speech effectively criminalised. We see violent attacks on journalists.”
Reporters Without Borders ranks Azerbaijan a "predator of press freedom" in its annual review of 179 countries. The French media-freedom group reports incidents where websites have been blocked, independent news organisations hacked and the arrest of Azerbaijani journalists and commentators.
Institutions under attack
In relation to the attack on the Council, a Commission spokesman told EurActiv: “There is no such thing as a big single, one-off attack out of the blue that catches us by surprise.”
“We are not sitting around and then, wham! An incident happens," said Antony Gravili, spokesman for EU the commissioner responsible for inter-institutional relations, Maroš Šefčovič.
"The reality is that this is a war of attrition, it is an arms race.”