"Hell yeah, I would!" Mr Bush, whose White House campaign has been flagging , said in response to the ethical dilemma.
"You gotta step up, man."
Mr Bush, 62, acknowledged such a killing could have unpredictable consequences, but insisted he would nevertheless kill the baby Adolf.
"It could have a dangerous effect on everything else, but I`d do it - I mean, Hitler," Mr Bush said.
To underline the point, the younger brother of former President George W Bush tweeted out a link to the article, commenting: "Gotta do it."
The moral question was initially posed last month by the New York Times Magazine in a reader poll which prompted widespread ridicule.
Mr Bush`s stance puts him in line with most respondents to that survey (42% said they`d kill baby Hitler; 30% said no; 28% were unsure).
Social media greeted Mr Bush`s theoretical infanticide with a wave of criticism.
"How the hell is this a relevant question relatable to the current political situation in this country?" one person tweeted.
Another person, apparently referring to Mr Bush`s pro-life stance, tweeted: "So it`s not okay to kill babies, except for that one. Makes perfect sense."
One more person tweeted: "Would you also go back in time and now allow your brother to steal the presidency which led to 9/11 and the false Iraq invasion?"
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