The former Liverpool star, who reportedly earned £40,000 for each episode of Match of the Day last season, listed Spain, Germany, the Netherlands and Portugal as his semi-final tips for the tournament in an article posted on the BBC's website.
However, with the Germans, Dutch and Portuguese all in Group B, it is impossible for all three to get out of the group as only two teams qualify.
After football fans took great pleasure in revealing the mistake on Twitter and Facebook, the BBC removed the article and when it was reposted Hansen was left with just three predictions with the Portugal pick removed.
Of the 16 expert opinions listed by the BBC, Hansen is now the only person who has selected just three potential semi-finalists.
Match of the Day host Gary Lineker took to Twitter to defend his colleague and blamed the website for the error and not Hansen.
"Alan Hansen's not as daft as some of you were hoping. They were his top four contenders, not his four semi-finalists," he tweeted.
"To doubters, I was at the press conference. We were asked for the winners, two challengers and dark horses. This was not interpreted correctly on the website."