The stopper was on Plymouth's pre-season tour in the Netherlands when he is said to have suffered the injury during a training session on Tuesday morning.
Burgoyne has now flown back to the UK for treatment and is expected to be on the sidelines until mid-October.
Taking to Twitter, the keeper wrote: "Gutted to have broken my ankle out in holland on pre season with @Only1Argyle I was so excited for the start of the season! But this is football and life and i will be back stronger than ever!! #greenarmy"
Burgoyne has been part of the Wolves youth setup since the age of 12.