The 30-year-old required surgery after damaging his right ankle during training with club side Saracens, which confirmed on Thursday (AEDT) he will be sidelined for eight to 10 weeks.
Farrell has not played since another ankle injury sustained during the November Test victory over Australia at Twickenham.
The news is a significant blow to Jones' plans, with Farrell having been earmarked to play at number 12 and act as a guide for inexperienced fly-half Marcus Smith.
"Owen has had his operation, so he'll be out of the Six Nations," Jones said.
"[It is a] massive blow for him personally, but it's a chance for people to step up. It's an opportunity for other people to fill those leadership roles and an opportunity for other players to play for that number 12 jumper.
"In today's rugby, it's rare that you have all your best players on the field. We're used to it.
"Last night we had to leave the hotel because of a fire outside, so the boys are adaptable. They know how to get along with things and there's an opportunity there to build a little more leadership depth."
George Ford had already been recalled to the squad following injuries to Farrell and Jonny May, who has a knee problem.
England's preparations for the clash in Glasgow were further disrupted by a positive COVID-19 test for Joe Marler, while Courtney Lawes – among the favourites to deputise for Farrell as captain – has been sitting out training because of head injury protocols.
The team were also evacuated from their hotel in Brighton after a suspected electrical fire nearby.
England begin their campaign against Scotland at Murrayfield on February 5 before facing Italy in Rome a week later.