Cech was injured when he fell under the weight of a colleague during training this week and Villas-Boas must now decide whether Hilario or Ross Turnbull should replace the Czech Republic international.
The new manager would have preferred to avoid making an enforced change to his defensive unit as he seeks his first Premier League win having been held to a scoreless draw by Stoke City in the opening game.
West Brom are unlikely to pose a similar physical threat as Stoke, but Villas-Boas is anxious to get Chelsea’s title challenge underway.
"Petr Cech suffered a medial ligament injury and will be out for three to four weeks," said the manager.
"It was the end of training, normal training incident. He fell awkwardly with his weight on top of him and he stretched a little bit the medial ligament.
"We expected much worse when we saw the incident. He's made the MRI and the good news is it's just three to four weeks."
Villas-Boas' options will be strengthened for the West Brom game by the arrival of Reomelu Lukaku from Anderlecht and the teenager will go straight into the squad but defender David Luiz will again be missing with a thigh problem.
With a trip to Old Trafford to face Manchester United looming in mid-September, Villas-Boas is anxious to have accumulated as many points as possible before the meeting with the champions.
And this game followed by another home fixture against newly promoted Norwich, the manager is targeting six points from the next two outings.
"We have two games at home that we must do everything in our power to get three points out of both, because it's seven points and can get us into a good position," he added. "It's two games at home and you have to win them.
"West Brom, as you saw last week (against Manchester United), provokes a very, very difficult challenge, because they held Man United - the Champions League finalists - up to the 80th minute."
West Brom were thrashed 6-0 at Stamford Bridge on the opening weekend of last season when Chelsea assistant manager Roberto Di Matteo was still the Baggies manager.
His successor, Roy Hodgson, has made them a more solid unit, however the veteran coach has warned they face a challenge every bit as tough as that presented last weekend by United, who required a late goal to beat them 2-1.
"I think we showed against Manchester United we are not a bad football team," Hodgson said.
"I know people will flag up last year, it went badly for us, but you can't turn back the clock. Our aim is to go there and get a positive result, which is anything from a draw to a win.
"My message to the players is it will be every bit as tough and we will have to work every bit as hard as against Manchester United to stand a chance."
Hodgson also said the Baggies remain hopeful free agent Owen Hargreaves will agree to join them following further discussions with their sporting and technical director Dan Ashworth.
"Dan has had further talks with him and they have been relatively positive," Hodgson added. "I don't know if further talks are planned but we believe he's capable of playing top-flight football again and we're very interested in him. "
The Baggies will make a late decision on whether striker Peter Odemwingie (ankle) is fit to play, two days after the Nigerian agreed a new three-year deal with the club.
Gareth McAuley could return after illness but Jerome Thomas (groin) and Zoltan Gera (suspended) miss out again, however.
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