Speaking to The Times, she said that Brexit should be managed by "serious people" and that being overly optimistic about the process "sells people short" - although she denied she was talking about Mr Johnson.
Miss Davidson, tipped as a potential Tory leader has clashed repeatedly with Mr Johnson in the past.
With regards to the single market, Mr Johnson said the United Kingdom should not pay for access after March 2019, and neither should it commit to mirroring European court rulings in exchange for access.
According to recordings published by Brexit Central, he added: "It is only now, after 44 years, that we're finally taking back control of our tariffs..."
He reiterated this sentiment in The Sun, telling readers: "The crucial thing I want to get over to Sun readers about Brexit is that it is going to be great and we need to believe in ourselves and believe we can do it". On Friday, he praised a speech by May in which she set out her plan for a roughly two-year transition period after Brexit.
She said: "I think optimism, positivity is good".
"What that teaches me is that really is it. Rien ne va plus". There can be no monkeying around.
He told the Sun: "I want people to be paid more". Yes, absolutely. Do I want the delay to go on longer than two years?
With most polls putting the Tories and Labour neck and neck, May said a vote for Jeremy Corbyn as prime minister was too risky.
The prime minister faced calls to discipline Johnson earlier this month after he laid out his own vision of Britain's future outside the European Union in a 4,000-word article for the Sunday Telegraph newspaper.
Brexit Secretary David Davis was backed by just 11% of Tories, falling from the top spot in July.
His latest intervention will revive fears in No 10 that Mr Johnson may storm out of the Government and position himself as a "Brexit martyr".
Johnson, in an interview, called for four conditions for Brexit: transition period must be a maximum of two years; United Kingdom must refuse to accept new European Union rules during that period; no payments for access to the single market after the end of the transition period; and United Kingdom must not agree to shadow European Union rules to gain access to the single market, BBC reported.
During that time, he said the United Kingdom should refuse to accept any new European Union or European Court of Justice rules.
"But when it comes to paying for access to the market, that won't happen any more than we would expect them to pay us for access to our market". That is the worst of both worlds.