The issue has divided political parties and provoked a fierce debate about public health and individual freedom.
More than 700 senior doctors last week backed a legal ban, saying that being in an enclosed space like a car significantly worsened the harm done to children by cigarette smoke.
On the other side of the argument, opponents said the ban would unnecessarily extend the power of the state further into private matters.
The proposed ban was put to Parliament by the Labour Party, and endorsed by the House of Lords last month.
Labour will back the move in the Commons, and Coalition MPs will be given a free vote.
Jeremy Hunt, the Health Secretary, and Michael Gove, the Education Secretary, are expected to vote for a ban.
Nick Clegg, the Deputy Prime Minister, is expected to be joined by several other Liberal Democrats in opposing it.
Mr Clegg, a smoker, has said that a legal ban could not be effectively policed. However, Norman Lamb, the Liberal Democrat health minister, supports the change.
Dr Penny Woods, the British Lung Foundation's chief executive, said a ban on smoking in cars carrying children is successfully enforced in several countries, including Canada and Australia.
She said: "MPs have a real chance of making history by voting to give children in the UK the same protection."
Dr Woods added she hoped "common-sense will prevail".
Robert Goodwill, the transport minister, told MPs last week he would vote in favour of the ban, having been forced to sit in the back of a car as a child while his father smoked.
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