Gallas has spent the start of this season on the sidelines but had appeared to be closing in on a comeback after completing 90 minutes in a friendly against Brentford last week.
Harry Redknapp hoped to recall the defender for Thursday's Europa League clash at home to Shamrock Rovers, with an eye to getting him match fit to face Arsenal.
However, Gallas has now suffered a fresh injury, to his other calf, and will not be able to take his place in what is likely to be a youthful-looking Spurs line-up against the Irish side at White Hart Lane.
While the new problem is not thought to be serious, Redknapp concedes the Frenchman is now highly unlikely to be available for Sunday's clash with the Gunners.
"William was looking OK to return but, just when we thought he was over his initial calf injury, he has pulled a calf muscle in the other leg," Redknapp said in The Sun.
"He won't face Shamrock and has virtually no chance of playing Arsenal. It's a shame because he turned in a man-of-the-match performance against Arsenal last season."
Watch Tottenham v Arsenal live on Sky Sports 1 and HD1 from 4pm on Sunday.
Source: Team Talk
Source: Team Talk