The MPs criticised him for borrowing heavily on the replies given by other members of the MPC at their confirmation hearing when he filled out a questionnaire. The committee approved the appointment of Dr Wadhwani, who joins the MPC next month.
But in its report it said: "We hope he will remember he is a member of the MPC as an individual with individual responsibility and independent views."
A source close to the committee described the rebuke as "a slight bollocking".
Mr Wadhwani escaped an attempt by Brian Sedgemore, a Labour MP on the Treasury Select Committee, to block his appointment on the grounds that he did not show the "necessary personal independence to serve on the MPC".
Mr Sedgemore had accused Dr Wadhwani of "letting down the Chancellor and insulting the committee" during a heated exchange during Monday's confirmation hearing.
Dr Wadhwani apologised to the committee, saying he copied replies where he agreed with the point, because he wanted to avoid speculators "nit- picking" over his choice of words.