A website ad showed three images, including one where three women were standing close together and partially covering each other's breasts with their arms.
The online ad described its Page 3 models as the "best, brightest and bubbliest girls around" and offered up the chance for two of them to visit someone at their workplace in return for explaining in 50 words or less why they should win.
The newspaper ad on the front page of the Daily Star showed a photo of two women wearing bikinis, alongside the text, "WIN a chance to meet our fab Page 3 girls".
On page three of the paper there was a photo of three women wearing only bikini bottoms with the text, "spend a day with a p3 babe".
The ASA received 31 complaints, one of which was from the Object, a group that campaigns against the use of women as sexual objects in the media.
Many of the other people who complained heard about the competition on social media.
In its response the Daily Star said the ads featured models who were in the paper regularly and seen as celebrities. It also said that win a date was used as "social meetings between individuals" and did not carry a connotation of "sexual activity".
However, the ASA found that the use of phrases such as "star babes" and a "sizzling prize", as well as the fact they were employed as page three models based on their attractiveness, meant that the prize would be enjoyed on the basis of their attractiveness rather than their personality.
The watchdog also decided that because the ads described the prize as involving "one of our babes" and "two of our top Page 3 girls", rather than specific models, the implication was that they were interchangeable.
The ASA ruled that although the Daily Star readers might not object to the concept of "Page 3", some would find the notion of offering women as a prize to be sexist, offensive and socially irresponsible.
The ads breached the rules on responsible advertising, harm and offence, and 8.7 sales promotions. They must not appear again in their current form.
The ASA also warned the Daily Star to make sure its future advertising did not contain anything that was socially irresponsible or likely to cause serious or widespread offence.