Paul Givan said his department does not have enough money to cover meal costs outside of school terms.
Speaking to the BBC's Good Morning Ulster programme ahead of the vote, he warned other education services would have to be cut to fund meal payments.
"The problem with [Baker's] private member's bill is that this funding doesn't come from the Department of Finance," Givan said.
"It is a Sinn Féin private member's bill with a Sinn Féin finance minister that are literally picking the pocket of the Department for Education to pay a welfare payment."
He warned it will "require an annual commitment of nearly £25m to £30m" and challenged supporters to identify which services they would cut to pay for it.
"To take the funding out of special educational needs and maintenance programmes in schools in order to make a welfare payment to people that are entitled to free school meals is not a responsible decision," Givan added.
Last month, his department tabled amendments that would have given him power to delay its implementation, but these were rejected by a majority of parties.
Ulster Unionist leader Jon Burrows said his party would not support the bill, saying that it was "undermining" the executive's case for asking London for additional funding to solve its budget impasse.
Although the DUP and UUP are set to vote against the bill on Tuesday, Sinn Féin is expected to have enough support from Alliance and SDLP MLAs to ensure the bill passes.