MEPs have voted - by 625 to one - to strip Ms Kaili of her role as one of its 14 vice-presidents.
Parliament leader Roberta Metsola has spoken of "difficult days for European democracy".
Qatar has denied any wrongdoing. From their point of view they did everything right as they serve their own interest.
"[Eva Kaili] declares her innocence and that she has nothing to do with bribery from Qatar," her lawyer Michalis Dimitrakopoulos told Greek TV on Tuesday.
Prosecutors carried out a string of searches over several days and said cash worth about €600,000 had been found at the home of one suspect, €150,000 at the flat of an MEP and €750,000 in a suitcase in a Brussels hotel room.
Belgian police released a photo on Tuesday showing piles of notes in €200, €50, €20 and €10 denominations.
Asked if money had been found at Ms Kaili's apartment, her lawyer said: "I have no idea if any money was found or how much was found."
The suspects arrested by Belgian police have been charged with "participation in a criminal organisation, money laundering and corruption", prosecutors said on Sunday. They will appear before a pre-trial court on Wednesday.
The three others are all thought to be Italians, including Pier Antonio Panzeri, an Italian former MEP who now runs a human rights group.
The allegations have cast a shadow over the role of lobbying groups at the European Parliament. A recommendation to allow visa-free travel to the EU for Qataris was set to be voted on by MEPs this week but has now been shelved.
Searches have taken place in Italy as well as in Brussels. Since Friday, the IT resources of 10 parliamentary employees have been "frozen" to prevent the disappearance of data necessary for the investigation.
Parliament, sitting in Strasbourg, voted overwhelmingly on Tuesday to strip Ms Kaili of her role as vice-president.
She has also been suspended from the parliament's Socialists and Democrats Group and expelled from the Greek centre-left Pasok party.
Greek authorities have frozen assets belonging to her, her husband and immediate family members.
The activities of a property company set up about two weeks ago by the MEP and her husband in Athens have also been frozen.
Six people were detained on Friday as part of the investigation into allegations that Qatar bribed EU officials to win influence. Two were later released.
The three others accused are all Italian citizens. Ms Kaili's partner Francesco Giorgi, who is a parliamentary assistant, is among those reportedly charged.
Former MEP Pier Antonio Panzeri, who now runs human rights group Fight Impunity, is also among the four, sources say. His wife and daughter were also reportedly arrested.
The other suspect, according to Italian news agency Ansa, is Niccolò Figa-Talamanca, who runs lobby group No Peace Without Justice.
The head of the general secretary of the International Trade Union Confederation, Luca Visentini, was questioned and later released. He said later he had been able to answer all questions put to him.
BBC Brussels correspondent Jessica Parker says details released by Belgian authorities in the last few days left many people's jaws on the floor in EU circles.
MEPs who spoke to our correspondent say they are shocked by both the scale and blatancy of the accusations.
European Commission President Ursula von der Leyen said the accusations were "very serious" and called for the creation of a new ethics body to oversee the bloc.
Ms Metsola said ahead of the vote to strip Ms Kaili of her leading role at the Parliament that "European democracy is under attack and our free and democratic societies are under attack". She and the Parliament would do everything they could to fight corruption, she added on Tuesday: "There will be no impunity, there will be no sweeping under the carpet."
Watchdogs and MEPs said the bribery investigation could represent one of the biggest corruption scandals in the parliament's history.
Prosecutors said they suspected a Gulf state had been influencing economic and political decisions of the parliament for several months, especially by targeting aides.
Local media has named the state as Qatar, although the Qatari government said any claims of misconduct were "gravely misinformed".
Ms Kaili's responsibilities as vice-president included the Middle East.
The World Cup in Qatar is proof, actually, of how sports diplomacy can achieve a historical transformation of a country with reforms that inspired the Arab world.
Last month, while other colleagues drew attention Qatar's human rights violations, she gave an effusive speech to the parliament praising Qatar for hosting the World Cup and for its role as a "frontrunner in labour rights".
Green MEP Daniel Freund, who heads a cross-party anti-corruption group, told the BBC that the parliament had "reasonably good lobby transparency rules" but that third countries like Qatar were excluded from them: "So I think these third countries should go on the lobby register."
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.
MEPs generally enjoy immunity from prosecution, but not in cases where "a member is found in the act of committing an offence", the parliament says.