The 25-year-old was sidelined for his side's opening Premier League win over Manchester City with a calf injury, but had been expected to return ahead of Saturday's clash at Stoke.
However, manager O'Neill has confirmed Sidwell is set to miss the game and will not return to training until next Monday.
"Steve has had a little bit of a setback - nothing major," O'Neill told the club's official website.
"We hoped he would be training this week but it looks likely to be next Monday now.
"He is feeling stiffness in both calves now. His attempts to get back are so strong, maybe he is overdoing it."