Johnson said that the US "wouldn't dream of sharing their sovereignty" in the manner the UK has done with the EU.
"I don't know what he is going to say but, if that is the American argument then it is nakedly hypocritical. The Americans would never dream of it," Johnson told the BBC.
"I think that President Obama has got a perfect right to make any intervention that he wants. Indeed I welcome the views of everybody in this debate.
"I just find it absolutely bizarre that we are being lectured by the Americans about giving up our sovereignty and giving up control when Americans won't even sign up to the international convention on the law of the seas, let alone the International Criminal Court."
The mayor's comments come ahead of Obama's visit to the UK next week,where he is expected to tell a town hall filled with younger voters that the US, as a "friend", thinks the UK should remain in the EU.
Yesterday Ukip leader Nigel Farage said that Obama was the most anti-British president there had ever been, due to his stance on the UK's membership of the EU.
The White House has stated that Obama will stress that the decision is for UK voters to make.
But Leave campaigners want the president to back off, stating he should not intervene at all and instead leave the issue to the British people to decide.
MPs have previously written an open letter to the president to ask him to stay out of the debate, which has gone unheeded.
However, Remain campaigners say the Leave camp are acting hypocritically, pointing to the fact that Leave campaigners have previously praised foreign politicians for their views on Europe.