Convert a composite bash string into json map

I have the following bash string

VAR="Minor:3.9,Full:3.9.10,Minor:3.8,Full:3.8.11,Minor:3.10,Full:3.10.11"

Is there a way (preferably through jq) to produce the following json object

json [ { "Minor":"3.9", "Full":"3.9.10" }, { "Minor":"3.8", "Full":"3.8.11" }, { "Minor":"3.10", "Full":"3.10.11" } ]