The club had feared the winger had broken his ankle against Norwich but initial scans show no obvious break and the 26-year-old will have further scans on Monday
Dyer was withdrawn after 44 minutes following an innocuous challenge with home captain Sebastien Bassong at Carrow Road on Sunday and taken to hospital.
While there were fears that the 26-year-old could be set for an lengthy injury lay-off, Swansea have confirmed initial signs are positive.
On their official Twitter account, the club said: "Initial x-ray shows no obvious break to Dyer's ankle.
"However, he will have further scans tomorrow [Monday] before final diagnosis."
Dyer had put Swansea ahead in the game before Gary Hooper secured a point for Chris Hughton's men with a stunning effort in first-half stoppage time.