The Wimbledon champion's mother believes the move would help combat childhood obesity.
She spoke out in support of a new study that warns that today's kids are the first to grow up 'less fit and healthy' than their parents.
Researchers found that more than one in 10 children were now classified as obese and a fifth had low fitness levels.
The report said that parents must be encouraged to take an 'active interest' in children's fitness rather than being 'overly-reliant' on schools to take care of the problem.
Tennis coach Judy said the Government should introduce compulsory 'physical education homework' to improve their activity levels outside of the school day.
The report, published by Ukactive, which represents the health and fitness industry, recommended a series of basic activities that parents could do with their children around the home and garden.
This included ball-throwing games, skipping, sprinting challenges, balancing and even jumping over furniture.
Writing in the foreword of the report, Judy said: "Modern diets and the multitude of sedentary activities that kids are used to certainly do not help, but it is the fact that children are not developing the basic aptitudes for sport and exercise that is the most worrying thing for me.
"It is vital that parents encourage and foster an environment where activity is considered important, but it is also vital for schools, sports providers and authorities to give parents the tools they need to instigate this process.
"It should be a national priority to re-embed children's physical literacy into the consciousness of parents in the same way they would monitor their children's homework."
She added: "Real change could be achieved by calling on government to include physical education homework as mandatory."
The report – Stay Young, Stay Active – said that the 'steady decline' of active lifestyles in school-age children was 'inexcusable'.
It said parents should also be issued with guidance on 'physical literacy' by health workers when they leave hospital after giving birth, it said.
The study added: "Parental involvement in the monitoring and development of their children's physical literacy should be considered to be as important as parental support for homework."
Judy has endorsed a series of 14 games parents can play with their children to improve fitness levels.
This includes bouncing balls off the wall to improve reaction and movement skills, obstacle course-style challenges, throwing different size balls into buckets to boost co-ordination levels and jumping over household objects.