The challenge aims to promote the benefits of active travel, including helping to reduce carbon emissions and boosting health and wellbeing.
Schools have been invited to share posts on social media which illustrate how they are taking part, with prizes for the most engaging and innovative.
Cllr Jim Foreman, Lead Member for Housing and Transport, said: "Many journeys that people make using cars are under five miles, so there's real potential to swap the car for walking and cycling.
"Choosing an active mode of transport not only provides opportunities for children to develop their road safety skills, but it also helps tackle congestion, reduce air pollution and decrease traffic danger outside the school gates.
"Using more sustainable forms of transport helps drive down carbon emissions and supports our move towards a greener, cleaner borough."
The competition is running throughout May and the winning school will receive £2,000 to be spent on future active travel initiatives. There are further prizes of £750, £500 and £250 for runners up.
Cllr Adam Ellison, Lead Member for Children, Young People and Families, said: "Walking, cycling or scooting can make the journey to school a lot more enjoyable and has proven benefits on mental wellbeing, meaning that children can enter the classroom with a positive attitude and a willingness to learn."
Schools are being asked to use the hashtag STactivetravelchallenge and tag @LoveST when they share posts on social media.
Ali Conway, Digital and Wellbeing Lead at St Oswald's CE VA Primary School in Hebburn, said: "The children have been doing a lot of work about climate change and feel very passionately about taking steps to combat it, so we were really keen to get involved in the active travel competition.
"We promote cycling, walking or scooting to school because of the benefits for both children and adults, for physical and mental health."