Woakes, who last played for England in the third Test against West Indies in March, was already ruled out of the first Test against New Zealand at Lord's next week but hoped to come into the three-match series later in June.
However, the 33-year-old looks unlikely to play a part, adding to England's injury crisis with seven fast bowlers out at the moment.
"He (Woakes) has been struggling with a longstanding knee injury and has also had a little ailment with his ankle, but it’s the knee injury that is holding him back," Warwickshire coach Mark Robinson said.
"At the moment there is no timescale on when he will be back."
England, who will be led by new captain Ben Stokes, are already missing the likes of Sam Curran and Mark Wood, while Jofra Archer was last week ruled out for a lengthy period due to a stress fracture of the back.