Two complaints to the watchdog complained that the advert claimed that "all the parts of the internet are on the iPhone".
The ASA said that because the Apple iPhone did not support Flash or Java - two programs that form part of many webpages to make them more interactive and feature-rich - the advert's claim was misleading.
When using the iPhone's Safari web browser to view internet pages, users see a different and less feature-rich version of the internet, said the ASA.
Apple had argued its internet access claim referred to availability of webpages, rather than their specific appearance.
But the ASA said the advert "gave a misleading impression of the internet capabilities of the iPhone".
The advert must, therefore, not be aired again in its current form, it said.