And it looks unlikely that the 20-year-old will recover in time for Wales' two-Test summer tour to Japan.
Wales play Japan in Osaka on June 8 and then in Tokyo seven days later, when Walker would have challenged strongly for a starting berth given the likely British and Irish Lions selection of his fellow wings George North and Alex Cuthbert.
Walker, one of the most lethal finishers in this season's RaboDirect PRO 12, was part of Wales' RBS 6 Nations squad this season.
Ospreys head physiotherapist Chris Towers confirmed that Walker had an operation on Tuesday.
"Eli hasn't shown any improvement following conservative treatment of his back issue, so having taken expert advice he underwent an operation to correct the problem on Tuesday," Towers said.
"Experience of dealing with similar issues suggests that he will be out of action for around 10 to 12 weeks."