A spokeswoman for the company told CNN that the products had already been removed from stores and on the Target.com website.
She said no incidents of suffocation were reported.
The withdrawal covers about 299,000 overalls that were put up for sale between July 2019 and October 2020, the agency said. The jumpsuits came in a range of styles in sizes ranging from newborn to 12 months.
The agency received 16 reports of tearing, detachment or missing from the overalls, including a report of scratches and another child who was pinched.
There were 27 reports of breaking or detaching snaps from swimsuits, including a single laceration.
About 181,000 swimsuits were mentioned. They were sold between December 2019 and October 2020 in sizes between 12 months and 5Q.
Customers who have purchased the product can call customer relations at 800-440-0680 or return the products to a store for a refund.