It is hoped the Tesco partnership will raise £1.5m to help disabled children gain independent mobility.
I Can wants to raise £1m through HBOS staff fundraising activities for its work with children who have complex and severe disabilities. It provides specialist therapy and education, information for parents and training, and advice for teachers and professionals.
In HBOS's Million Pound Challenge, any money raised above the £1m mark will be split between I Can and the other two shortlisted charities, Leonard Cheshire and Crisis. They will also receive £25,000 immediately from HBOS, leaving the fundraising activity focused on I Can.
The children's charity will use any money raised to help 1,200 nurseries train experts to provide help and support for children with communication disabilities.
Virginia Beardshaw, chief executive of I Can, said: "This will make a huge and lasting difference to the lives of children across the UK who struggle to communicate. It will have a transforming effect."
Whizz-Kidz has 391 disabled children on its waiting list, and £1.5m would provide every child on it with their own customised wheelchair.
The partnership was launched at Tesco Kensington on Monday, with an alternative version of Supermarket Sweep.
Two Whizz-Kidz beneficiaries raced against the clock to collect groceries, demonstrating the importance of their customised mobility equipment in helping them be more independent. A non-disabled person then made the dash in a standard, non-customised wheelchair to demonstrate how difficult the task can be without bespoke equipment.
Ruth Owen, chief executive of Whizz-Kidz, said: "It's the biggest pitch we could have won from the corporate sector. It is very competitive, and it's hard to put into words how much this means for the charity."
Whizz-Kidz made its original pitch to the supermarket giant in March 2005. As well as raising money, the partnership will boost awareness of the charity in communities across the UK.