Facebook boss Mark Zuckerberg's decision not to appear before MPs is "astonishing", said the committee chairman who invited him to attend.
Damian Collins, the head of a parliamentary inquiry into fake news, urged Mr Zuckerberg to "think again".
Facebook and data analytics firm Cambridge Analytica are at the centre of a row over harvesting personal data.
Mr Zuckerberg has apologised for a "breach of trust", but said he will not appear in front of the inquiry.
He will instead send one of his senior executives, Facebook's chief product officer Chris Cox, who will give evidence to MPs in the first week after the Easter parliamentary break.
The global reach of Cambridge Analytica
What does Cambridge Analytica do?
Facebook data sharing - time to act?
Mr Collins, the chairman of the Department for Culture Media and Sport select committee, said: "Given the extraordinary evidence that we've heard so far today... it is absolutely astonishing that Mark Zuckerberg is not prepared to submit himself to questioning.
"These are questions of a fundamental importance and concern to Facebook users, as well as to our inquiry as well.
"I would certainly urge him to think again if he has any care for people that use his company's services."
Facebook said Mr Cox was "well placed to answer the committee's questions".
At the weekend Mr Zuckerberg took out full-page advertisements in several UK and US Sunday newspapers to apologise, adding the company could have done more to stop millions of users having their data exploited by Cambridge Analytica.