Tajani said: "Our citizens deserve a full and detailed explanation".
European Union justice commissioner Vera Jourova, who is in charge of the bloc's new privacy rules, welcomed Zuckerberg's decision to travel to Brussels in person, but said she regretted the meeting will happen behind closed doors.
"The Conference of Presidents has agreed that Mark Zuckerberg should come to clarify issues related to the use of personal data in a meeting with representatives of the European Parliament", Tajani said in a statement.
Meanwhile, Facebook's head of public policy in the UK, Rebecca Stimson, wrote to Damian Collins MP, chair of the Digital, Culture, Media and Sport (DCMS) select committee, this week to confirm Zuckerberg "has no plans to meet with the committee or travel to the UK at present".
While Zuckerberg testified last month to the U.S. Congress, he had always been noncommittal on his appearance in Europe, sending his chief technical officer to speak to the British parliament and delaying confirmation of any visit to Brussels.
That suggests he will avoid an uncomfortable public appearance and instead meet only with the legislature's top brass behind closed doors.
The meeting comes ahead of the enforcement of new European data protection regulations coming into force on May 25th. "It is a step in the right direction towards restoring confidence", he said.
Members of the public also won't be able to form their opinions about Zuckerberg's answers to the members of the parliament.
Justice Commissioner Věra Jourová was admonished by Tajani when she said it was a pity the hearing would not be public.
Cambridge Analytica said it pitched to Leave.EU, a Brexit campaign group, but did not do any work for them after it missed out on the official campaign designation to Vote Leave, which is separately being investigated for possibly breaches of campaign finance rules.
Zuckerberg has so far declined to appear, to the British lawmakers' annoyance.
The 40-page letter, in response to the committee's formal request for Facebook to respond to 39 points it felt Facebook CTO Mike Schroepfer answer answered unsatisfactorily last month when he appeared before MPs, arrived three days after an initial 11 May deadline - with Facebook requesting, and being granted, an extension.