The frontrunner in the race to become prime minister committed on Wednesday to review the effectiveness of such taxes and to ask whether they unfairly hit those on low incomes.
The Tory MP also vowed not to introduce new ones until the review has been completed, as he hailed Brexit as an opportunity to examine tax policy.
Mr Johnson's campaign cited taxes on products high in salt, fat and sugar as examples.
His team did not immediately respond to requests as to whether the review would also include cigarettes and alcohol taxation.
It also coincides with the launch of a high profile campaign by Cancer Research UK warning that obese people outnumber smokers by nearly two to one in Scotland.
As London mayor in 2016, Mr Johnson introduced a 10p levy on all added-sugar soft drinks sold in the City Hall cafe saying tackling obesity, was "one of the biggest" health challenges.
Mr Johnson said: "The recent proposal for a tax on milkshakes seems to me to clobber those who can least afford it.
"If we want people to lose weight and live healthier lifestyles, we should encourage people to walk, cycle and generally do more exercise.
"Rather than just taxing people more, we should look at how effective the so-called 'sin taxes' really are, and if they actually change behaviour.
"Once we leave the EU on October 31, we will have a historic opportunity to change the way politics is done in this country.
"A good way to start would be basing tax policy on clear evidence."
Cancer Research UK called on the Scottish Government to take action on junk food price promotions.
The sugar tax on soft drinks was introduced in April last year, and has been celebrated by experts including the Royal College of Paediatrics and Child Health.
Gregor McNie, Cancer Research UK’s head of external affairs in Scotland, said: “There isn’t a silver bullet to reduce obesity, but the huge fall in smoking over the years – partly thanks to advertising and environmental bans – shows that government-led change works. It was needed to tackle sky-high smoking rates, and now the same is true for obesity.
“The Scottish Government must do what it can to make it easier for people here to live a healthier life. In its next Programme for Government, a commitment to introduce laws to restrict the junk food multibuy price promotions that tempt us to eat too much would go a long way to helping us to do a healthier shop.”
The Obesity Health Alliance's Caroline Cerny said voluntary programmes for the food industry to cut sugar "have not had the same success" as the tax.
"The levy is supported by the public and welcomed by a wide range of health experts and is vitally needed as part of a package of measures to help create a healthier environment for everyone," she said.