Despite criticism of his form during 2021-22, the England international has been back to his best during the opening weeks of the new campaign.
Pickford has conceded just six goals in as many matches, including keeping a clean sheet during the Merseyside derby against Liverpool last weekend.
The 28-year-old produced one of his standout performances since his arrival at Goodison Park, with two of his saves seeing goal-bound efforts from Darwin Nunez and Mohamed Salah tipped onto the work.
However, according to The Athletic, Pickford will now miss a minimum of two Everton matches as he recuperates from the issue.
Frank Lampard's side are next in action on Sunday when they square off against Premier League leaders Arsenal before they play host to West Ham United before the international break.
If the injury is confirmed, Pickford will almost certainly miss England's UEFA Nations fixtures towards the end of the month as well.
As it stands, the report suggests that the best-case scenario is a return to action when his club meet Southampton in the top flight on October 1.
Everton's goalkeeping situation is further complicated by third-choice Andy Lonergan also currently sidelined with a knee problem.
Asmir Begovic is in line to deputise for Pickford for the foreseeable future with the 35-year-old having made a total of eight outings since his arrival last summer.
Coincidentally, the last of Begovic's three top-flight outings came at Arsenal last season, the Bosnia-Herzegovina international featuring in a 5-1 defeat on the final weekend.
However, Begovic does have game time under his belt during 2022-23 having kept a clean sheet in the EFL Cup tie at Fleetwood Town on August 23.
Zan Luk Leban appears likely to be promoted to the substitutes' bench with the 19-year-old making five starts for the Under-21s this campaign.