The 28-year-old suffered damage to her ankle ligaments from a tackle during the friendly game against Celtic earlier this month.
She will now enter a period of rehabilitation with no timescale set for her return.
The Republic of Ireland international joined the Reds in June after five years at Manchester City and sent a message to supporters after the surgery was completed.
“I’m heartbroken that I will have to wait to pull on the Liverpool shirt for the first time in a competitive game, especially with the fans returning on Sunday,” said Campbell.
“But it is a long season and I’ll be working as hard as I can to be back with the team in what will be an important year for the club.