Send mulberries through a food mill to remove seeds and excess pulp.
Combine mulberry juice, ginger and sugar in a large saucepan.
Bring to a full rolling boil, boil for 1 minute, skim foam off the syrup and discard.
Remove from heat and fill jars leaving 1/2-inch head-space.
Wipe rims of jars clean with a warm wash cloth. Place lids on jars and tighten rims.
Process in a boiling water canner for 10 minutes.
Remove jars carefully with a jar remover.
Place hot jars on counter top.
As jars cool you'll hear a "ping" when the jars seal.
Leave undisturbed for 24 hours.