It warns that even baby food marked "no added sugar" often contains sugars from honey or fruit juice.
Parents should offer bitter flavours too, the Royal College of Paediatrics and Child Health recommends.
This will guard against tooth decay, poor diet and obesity.
The recommendation is one of many included in a report on how to improve the health of children in the UK.
Reducing child obesity is a key priority in all parts of the UK, with England and Scotland committing to halving rates by 2030.
Targeting food high in sugar and fat is an important part of that aim, following the introduction of a tax on sugary drinks in England in 2018.
The report says the government should introduce mandatory limits on the amount of free sugar in baby foods.
Many can contain high levels of sugar added by the manufacturer or present in syrups and fruit juices, it says, despite labels suggesting otherwise.
The report says infants should not be given sugary drinks. Instead, they should have sugar in a natural form, such as whole fresh fruit, milk or unsweetened dairy products.
Prof Mary Fewtrell, nutrition lead for the Royal College of Paediatrics and Child Health, said products for weaning babies often contained a high proportion of fruit or sweet-tasting vegetables.
"Pureed or liquid baby foods packaged in pouches also often have a high energy density and a high proportion of sugar," she said.
"If sucked from the pouch, the baby also misses out on the opportunity to learn about eating from a spoon or feeding himself.
"Baby foods can be labelled 'no added sugar' if the sugar comes from fruit - but all sugars have the same effects on the teeth and on metabolism."
'Broccoli and spinach'
She said babies had a preference for sweet tastes but parents should not reinforce that.
"Babies are very willing to try different flavours, if they're given the chance," Prof Fewtrell said, "and it's important that they're introduced to a variety of flavours, including more bitter tasting foods such as broccoli and spinach, from a young age."
Prof Fewtrell also said parents should be educated on the impact of sugar.
"Excess sugar is one of the leading causes of tooth decay, which is the most common oral disease in children, affecting nearly a quarter (23%) of five-year-olds."
She added that sugar intake also contributed to children becoming overweight and obese.
The Scientific Advisory Committee on Nutrition recommends sugar provides no more than 5% of daily total energy intake for those aged two and over, and even less for children under two.
But results from the National Diet and Nutrition Survey suggest the average daily intake for the children between one-and-a-half and three years is 11.3% - more than double the recommended amount.
A review of food and drinks aimed at young children, by Public Health England, found that processed dried fruit products contained the highest amount of sugar - but were often marketed as healthy snacks.
The products, which contain fruit juices, purees and concentrates, making them high in free sugars, should not be sold as suitable snacks for children, PHE said.
