Plymouth Associates "irresponsibly placed" two adverts of naked women in the app My Talking Tom, the Advertising Standards Authority (ASA) said.
Two parents complained after children aged seven and three saw the adverts while playing the game.
The company denied responsibility for placing the adverts in the mobile app.
My Talking Tom features an animated cat, which players can adopt and look after.
The subject of the ASA complaints were two pop-up ads that appeared in the My Talking Tom app between 6 and 9 August 2015.
The adverts promoted Affairalert.com - which is the name Plymouth Associates trades under - and featured "a selfie of a naked woman sitting in front of a mirror".
The adverts asked the viewer if they wanted to have sex with the woman, giving them options of "yes", "no" and "maybe".
Plymouth Associates, which is based in Anguilla, denied responsibility and said it took its social responsibilities seriously.
It said it "had no role in placing or commissioning any ad in, or with, the My Talking Tom app" and suspected the adverts were placed by someone "seeking to damage Plymouth Associates' reputation" by means of inserting "malicious ad code".
Outfit7, which operated the app, said its apps were not directed at children, but it "strove to be family friendly" and had systems in place to categorise, filter and prohibit inappropriate or pornographic adverts.
However, Outfit7 said it was "impossible to eliminate the risk altogether" and technical malfunctions or human error "remained possible".
After the incident, Outfit7 could not identify which network was responsible for the adverts.
In its ruling, the ASA said the sexually explicit nature of the adverts meant they "should not have appeared in media which might be seen by children".
It said Plymouth Associates did not provide evidence to prove a third party placed the adverts, so the watchdog considered them to be responsible.
Additionally, while Plymouth Associates had procedures in place the ASA was concerned these "had not been adequate".
It told the company to make sure its adverts were targeted appropriately in future and did not target apps played by children.
"Sexually explicit" adverts which appeared in an app used by children breached industry code, the advertising watchdog has ruled.