The Prime Minister's "do or dry" pledge follows his failure to keep his "do or die" promise of taking Britain out of the EU by October 31.
Mr Johnson was pictured just yesterday sipping whisky during a distillery visit in Scotland, casting doubt on this commitment to a drinking ban.
His remarks about giving up alcohol came while chatting about health matters with nurses at the King's Mill Hospital in Nottinghamshire on Friday.
Mr Johnson asked them to tell him more about Ashfield, noting: "Someone said there's a lot of first-time mums who are smoking or something like that. Is that right?"
Mr Johnson was told a lot of people smoke in Ashfield before he switched his attention to vaping, saying: "I'm not certain about it.
"It might just encourage them to get into nicotine."
He then asked "what about alcohol?" before adding: "I've had to give it up until we get Brexit done."
Mr Johnson did not clarify whether he meant the first phase of Brexit by the end of January 2020 or the end of the transition period in December next year - or what would happen if the UK remained in the EU.
He was later given a tour of a school and tried to make a clay figure inspired by Sir Antony Gormley, whose works include the Angel Of The North.
Speaking at the George Spencer Academy, near Nottingham, Mr Johnson remarked he had "gunk" on him before declaring the task would be "a piece of cake".
But seconds later Mr Johnson paused before joking "it's all going horribly wrong" as he had not followed the guide and noted he was creating a figure similar to "Terminator".
He also told pupils: "He's an interesting chap Antony Gormley - all his sculptures are modelled on himself and then he persuades people to pay colossal sums for his own image around the world.
"It's amazing success he's had.
"We had a plan in the Olympic Games in 2012 to make a huge human being like this with steps sort of all the way up so you could walk up him.
"Gormley was going to do it but it was going to cost a huge amount."
Rachael Hodges, senior policy officer at the British Lung Foundation, said her organisation was glad the Prime Minister raised the issue of Mansfield and Ashfield's high smoking rates, but said his comments on vaping required clarification.
She said their research suggests smokers in Mansfield and Ashfield have been left struggling to access well-funded stop smoking services "due to years of government cuts to public health budgets".
She added: "To tackle this, the UK's next government must make public health funding a priority so local health services can ensure everyone has access to the best support to quit.
"Boris' comments on vaping also require clarification. Far from e-cigarettes encouraging nicotine addiction the evidence shows vaping is a very effective stop smoking tool.
"The vast majority who use e-cigarettes do so to quit smoking and e-cigarettes are one of many tools available to help quitters."