The ad by Dare has received 43 complaints since airing on Monday night, according to the Advertising Standards Authority (ASA), which said consumers called the ad offensive and had the potential of causing harm to children.
The advertising watchdog is in the process of assessing the ad and has not yet made a decision if investigation is necessary.
The ASA has the power to ban or place a scheduling restriction on the ad if it finds it could be harmful to children.
The ad shows Barker dressed in a balaclava aiming at Gio Compario with a bazooka, as he serenades a young couple in his signature style.
When the gun is fired, a crater appears where Compario was standing, but the missile has missed the singer.
The ad ends with the new strapline, "GoCompare: Saving the nation."
The ad, created by Dare, was preceded by a week-long teaser campaign across Twitter and outdoor.
Toby Horry, managing director, Dare, told Campaign: "Clearly no offence was intended because Gio Compario is a fictional character in a fictional world, and if the ASA gets in touch then we will act accordingly."
Follow Loulla-Mae Eleftheriou-Smith on Twitter @loullamae_es