The 28-year-old tight-head fractured the radius in his right forearm during Gloucester's 17-16 win over Bath at Kingsholm on Saturday and is only expected to be out for six weeks meaning he should be fit in time for the summer tour.
Vickery said: 'I've got the operation this afternoon and I could be back doing fitness work after a week.
"As frustrating as it is, I've got to be positive, and this isn't an injury that will stop me from working hard on the fitness elements and being around the lads.'
After the game, Vickery spoke with Bath prop David Barnes, who also broke his arm recently.
'I had a chat with David Barnes and it looks like a similar injury to him," he said.
"He said he had the operation and he was back running after a week.
'There's no doubt that I'm going to get involved and be around this place as soon as I can after the operation.'