Professor Robin May says guidance also advises that children under 10 should not be served free refills of the drink.
The warning comes after two children collapsed and almost died after drinking a slushie.
Beth Green revealed how her four-year-old son Albie was rushed to hospital after downing a strawberry-flavoured slush.
Ms Green claims doctors told her the episode was likely caused by glycerol intolerance after drinking the slush.
In an interview with Good Morning Britain on Tuesday (13 February), Professor May warned: “The issue is if you consume a lot of glycerol fast, particularly if you’re relatively small, a small child.”