Damian Collins, chair of the influential Digital, Culture, Media and Sport committee (DCMS), said the social media giant had previously given "misleading" evidence to Parliament and "consistently understated the risk" of user data being used without their consent.
The London-based political consulting firm was credited with aiding Donald Trump's 2016 US Presidential run and it was also employed by the Leave campaign during the EU referendum.
The letter states: "The committee has repeatedly asked Facebook about how companies acquire and hold on to user data from their site, and in particular about whether data had been taken without their consent.
"Your officials' answers have consistently understated this risk, and have been misleading to the committee.
"It is now time to hear from a senior Facebook executive with the sufficient authority to give an accurate account of this catastrophic failure of process.
"There is a strong public interest test regarding user protection. Accordingly we are sure you will understand the need for a representative from right at the top of the organisation to address concerns.
"Given your commitment at the start of the New Year to "fixing" Facebook, I hope that this representative will be you."