The 24-year-old sustained her injury in the melee after Chloe Hosking clipped the back wheel of Kirsten Wild, who was stripped of her win and disqualified.
Drops Cycling Team announced that Barker is now concentrating on making a full recovery, with the Welsh rider ruled out of the Tour of Scotland.
Barker defended Wild at the time of the incident, and the Rio 2016 track gold medallist said: "Thank you everybody for all the kind messages and to the team for their continued support.
I’m really gutted to be missing the Tour of Scotland this weekend, but surgery went well and I’m recovering quickly and hoping to be back on my bike early next week.
Barker was one of the riders involved in the crash - but she was in good spirits as she posted on Sunday: "They say you're not a real cyclist until you've broken a collarbone - avoided joining the club for 15 years but not much I could do yesterday."
Barker also defended Dutch rider Wild, saying that she believes the incident was an accident.
"A bit upsetting to see comments aimed at Kirsten though. It’s easy to criticise from a slow-mo aerial shot.
"The real time reality is that everybody is just hoping that their split second decision benefits themselves without harming anybody else. Race accidents happen."