The row comes after a Dutch radio station reported a leak of documents on international terrorism investigations by the agency, based in The Hague, Netherlands.
The station, 'Zembla', said Europol appeared to have failed to protect "very sensitive information."
European security union Commissioner Julian King and the director of Europol, Rob Wainwright, are now being asked to explain the allegations.
Sophie in 't Veld, ALDE group spokesperson for data protection, demanded that both appear in Parliament to explain and clarify the facts related to the reported leak.
The Dutch MEP said, "This is extremely shocking. Europol was aware of this security incident since September, yet its director decided not to inform the Parliament during a joint meeting of the European Parliament and the national Parliaments on Europol scrutiny just two days ago."
At the meeting, King admitted that, for the public, the agency "still needs to be seen as legitimate."
Wainwright, a former British police officer, explained the agency's latest work, including a crackdown on people smugglers.
But in 't Veld, speaking on Thursday, said, "This case proves once again that data protection is not an obstacle to security, but an absolute precondition. It is essential for information exchange and police cooperation.
"This leak damages trust in Europol and trust in information exchange, which is our top priority in the security agenda. Information sharing is essential for security."
In his appearance in Parliament this week, Wainwright made no reference to the reports of leaked intelligence, but insisted that Europol was providing "crucial" support to the fight against terrorism and organised crime.
He cited, as an example, "successes" in recent days, including the removal of 4500 illegal websites trading in counterfeit goods, as well the dismantling earlier this week of a major network of people smugglers in Spain.
He told the meeting, "Europol is not an FBI of Europe but, every single day, is proving practical benefits to member states and exchanges thousands of intelligence messages. Indeed, there has been a six fold increase in intelligence sharing in the last five years."
This had proved particularly useful in tracking the estimated 5000 foreign fighters who had left Europe to fight in Iraq and Syria, many of whom had now returned to Europe.
The agency chief told MEPs that the auditing and accountability standards to which Europol had to adhere to were "very high."