It is feared that the spout in the sports bottle cap may become detached causing a choking hazard.
The bottles being recalled have a batch code of NO5 L9164, NO5 L9171 and NO6 L9171 plus a best before date of March 2020.
Shops selling the affected Fruit Shoots will be displaying point-of-sale notices.
A spokesman said: "Britvic PLC is recalling selected Robinson's Fruit Shoot Apple and Blackcurrant bottles as a precautionary measure because of a small number of reports that the spout within the sports bottle cap may become detached unexpectedly, which may present a safety risk.
"The product was sold as multipacks (24 bottles) in Tesco and Costco, and as single bottles in McDonald’s, between 22 and 28 June."
Anyone who may have bought the Fruit Shoot is asked to dispose of the product safely and apply for a full refund via the Fruit Shoot Consumer care line on 0114 223 44 88 or via: https://fruitshoot.com/gb/contact-us/