The Republican front-runner supports a ban on abortions, with some exceptions.
Abortion has been legal in the United States since 1973 after a landmark Supreme Court ruling.
Only the Supreme Court or a constitutional amendment has the power to overturnRoe v Wade and make abortion illegal.
Analysis: Anthony Zurcher, BBC News North America reporter
The Republican party's official position is that abortion should be illegal. Conservative politicians and anti-abortion activists who view abortion as akin to murder, however, tend to avoid outlining any criminal punishment for women who undergo the procedure, instead targeting the doctors responsible.
The reason for this is simple - to make abortion bans more acceptable to a general public that does not want to see possibly distraught women grappling with unwanted pregnancies sent to prison.
Donald Trump, as he is wont to do, just trampled through this carefully constructed conservative political dance with all the grace of a rhinoceros at a tea party. Thanks to his assertion, after prodding, that women should face "some form of punishment" for having an illegal abortion, the conservative pro-life movement is going to be forced to defend their beliefs on uncomfortable ground. Republican candidates will be asked, again and again, to defend or denounce Mr Trump's comments.
This is exactly the kind of scenario that terrifies Republican politicians about Mr Trump as their party's nominee. His ill-considered remarks and shoot-from-the-hip approach to media interviews could be a political minefield for their candidates in the autumn.
In all likelihood it's just a taste of things to come.