Irish Foreign Affairs Minister Simon Coveney said the allegations are “extremely devastating.”
Authorities believe a Gulf nation – reportedly Qatar – tried to sway parliament through monetary or in-kind contributions.
Qatar has refuted any wrongdoing.
In 16 searches conducted in Brussels on Friday, Belgian police confiscated cash totaling roughly €600,000 ($632,000/£515,000). In order to investigate the contents, computers and mobile phones were also taken.
According to prosecutors, two people have been released while four have been charged.
Although no suspects have been publicly identified, Ms Kaili is believed to be one of those who have been charged.
They are accused of participating in a criminal organisation, money laundering, and corruption, according to a statement from the Belgian federal prosecutor’s office.
Ms Kaili, who has been a Member of the European Parliament for eight year, was relieved of her responsibilities as one of the 14 Vice Presidents by Roberta Metsola, President of the European Parliament.
She has also been kicked out of the Greek Pasok center-left party and suspended from the Socialists and Democrats group in the Parliament.
All of Ms. Kaili’s assets have reportedly blocked by Greek prosecutors.
The bribery inquiry, according to watchdogs and opposition MEPs, may be one of the largest corruption scandals in the history of the European Parliament.
As he arrived for a meeting of EU foreign ministers on Monday, Mr. Borrell told reporters: “The news is certainly very, very troubling.”
He added: “As a former president of the European Parliament, I can say with certainty that the events and circumstances we are currently confronting worry me.”
According to Mr. Borrell, the probe did not focus on any members of the EU diplomatic corps.
Before the meeting on Monday, Mr. Coveney added that “we need to get to the bottom of it” and called the accusations “extremely harmful.”
German MEP Terry Reintke, who serves as co-chair of the Green group in parliament, has demanded that Ms. Kaili resign immediately.
According to prosecutors, a Gulf state has been meddling in the political and economic decisions of the parliament for a number of months by targeting aides.
Although the state has been identified by local media as Qatar, the Qatari government has stated that any allegations of wrongdoing are “erroneous.”
The Middle East is one of Ms. Kaili’s Vice-Presidential responsibilities. She has previously stood up for Qatar.
Ms. Metsola took a flight on Saturday night from her native Malta to Brussels to witness the search of an MEP’s home, as required by Belgian law.
The European Parliament “stands firmly against corruption,” according to her spokesman, and is “collaborating” with the authorities.
The European Parliament is the EU’s only directly-elected institution. Some 705 members of parliament, elected by voters in the 27 nations which make up the EU, meet to scrutinise proposed legislation and vote through European law.