The former Yeovil hit-man was withdrawn at half-time of the Robins' victory at struggling Bury on Saturday with a calf problem and subsequent scans have revealed it will be several weeks until he regains match fitness.
"Andy Williams is one month at least," Di Canio told the Swindon Advertiser.
Williams will be joined in the Swindon treatment room by captain Alan McCormack.
The defender is nursing a hamstring complaint, which will definitely keep him out of the clash with Coventry this weekend.
However, Di Canio could welcome back winger Gary Roberts, who will resume full training with the first-team this week and, barring any adverse reaction, could feature against the Sky Blues.