Obesity is linked to a number of health problems
Children in England and Wales are currently measured at the ages of five and 10 but parents are informed of the results only if they request them.
But the figures may be given to parents automatically under the new plans.
The DoH said ministers were prepared to go further and faster in the fight against childhood obesity, although no firm decisions had been made.
Between a quarter and a third of children are thought to be overweight and doctors fear there will be an epidemic of poor health related to obesity in coming decades.
An obese person dies on average nine years earlier than somebody of normal weight, while a very obese person's life is cut short by an average of 13 years.
Under the proposals being considered, information obtained under the national measurement programme could be given to parents automatically.
And involvement in the measurement scheme may become compulsory unless people choose to opt out of the scheme.
Tam Fry, from the National Obesity Forum, said child obesity was a "huge problem to overcome".
He said: "It's a good thing in the sense that if the government expects parents to [have] prime responsibility for the raising of their children, it is absolutely essential that they should know what the healthy range of weight is.
"We would think, in fact, this whole thing has got to start earlier.
"If you start earlier, around the age of two and three from nursery, then you've got the time to start to implant the healthy eating, healthy exercise education, which will then carry them through school."
Mr Fry added that the Forum would even like to start to promote this mode of lifestyle "from conception".
A recent report by the Foresight Programme argued that dramatic and comprehensive action was required to stop the majority of us becoming obese by 2050.
Its authors predicted that if current trends continue, in that year, 60% of men and half of women will be obese and cases of type 2 diabetes will rise by 70%.
The report also suggested that cases of stroke will rise by 30% by the middle of the century and cases of coronary heart disease will rise by 20%.