The former Liverpool player was giving his thoughts during Argentina's 1-0 victory over Switzerland in their last-16 clash in Brazil on Tuesday.
After Swiss striker Josip Drmic unleashed a weak shot at goal, Lawrenson said that the player "should have put a skirt on".
Numerous viewers took to social media to express their shock at his comment during the game, which was won by Angel di Maria's extra-time goal.
The BBC released a statement saying: "We acknowledge that the remark by commentator Mark Lawrenson about Switzerland's Josip Drmic was inappropriate and we apologise for any offence caused by it."
Broadcasting watchdog Ofcom also received six complaints.