The Vauxhall Zafira car also contained the child's disabled blue badge.
It happened overnight in Kippax between Sunday, November 10 and Monday 11.
Officers are now appealing to the public to share this far and wide.
The WYP Leeds East team said: "Please can everyone help by sharing this far and wide
"Overnight in Kippax there has been a burglary where the following car has been taken silver Vauxhall Zafira YB67DLV
"The vehicle contained a wheelchair and blue badge for a terminally ill 6 year old boy."
Anyone with information should call 101 and quote crime reference number 13190578846.