The Swedish furniture retailer has stopped selling the drawers in the US and Canada after they toppled over and crushed the children.
Initially, Ikea warned customers to use wall mounts with them, but a third death in February prompted the recall.
The recall does not apply to the UK and Ireland.
The units being withdrawn are children's chests of drawers higher than 23.5 inches (60 cm) and adult chests of drawers and dressers above 29.5 inches.
In addition to the three deaths since 2014, Ikea had received reports of 41 tip-over incidents involving the Malm chests and dressers, resulting in 17 injuries to children between the ages of 19 months and 10 years old, the US Consumer Product Safety Commission (CPSC) said.
Ikea said that anyone who owns one of the pieces of furniture, and has not attached it to a wall, should take it out of the reach of children.
Consumers can choose between a refund or a free wall-anchoring repair kit.
The deaths caused by the toppling furniture prompted the CPSC to launch an education campaign to promote awareness of the problem across the industry.
Ikea said that it would help to promote the campaign in the US and around the world.
"With the Secure it! campaign, launched globally in stores and on Ikea's website, Ikea urges customers to inspect their chests of drawers and dressers to ensure that they are securely anchored to the wall according to assembly instructions," Ikea said in a statement.
The chairman of the CPSC Elliot Kaye added: "Today's announcement is not the end of our work on this hazard, nor should it be for the furniture industry.
"Ikea has several promising ideas to prevent injuries."
Ikea is recalling 29 million Malm chests of drawers in North America after the deaths of three children in the US.