MPs voted in favour of an amendment to the Children and Families Bill, which empowers, but does not compel, ministers to bring in a ban in England.
The vote - passed by 376 votes to 107 - also gave the Welsh government the power to bring in a ban in Wales.
Welsh ministers must now decide if they want to make smoking in cars carrying children illegal in Wales.
Liberal Democrat Health Minister Norman Lamb, speaking to BBC Radio 4's World Tonight programme on Monday, said he hoped a ban would be established.
He said the majority of 269 was "so decisive that I think there's a very clear mandate now to get on and legislate, but we will have that discussion".
He added, "You have to ask yourself the question, 'How important is the liberty that we're infringing here?'
"The liberty to smoke in your car in front of a child doesn't seem to me that important and protecting a child's health does seem to me to be incredibly important."
Department of Health figures from 2011 revealed that there were 300,000 GP visits and 9,500 hospital admissions that year as a result of children inhaling second-hand smoke.
The BMA praised Parliament's decision stating: “Smoking in private vehicles is a concentrated source of second-hand smoke and the act of smoking can also distract drivers from the road.
“We are pleased that MPs have taken an important step towards reducing tobacco harm.”
The Government is also looking to introduce legislation to make plain tobacco packaging compulsory.