Cech fell awkwardly during Wednesday's session and Chelsea will be hoping he returns in time for the Premier League trip to champions Manchester United on September 18.
Cech appears certain to miss the Czech Republic's Euro 2012 Group I qualifier tie in Scotland on September 3.
Villas-Boas said: "Petr Cech yesterday suffered a medial ligament injury and will be out for three to four weeks.
"It was the end of training a normal training injury, he fell awkwardly with his weight on top of him and stretched a little bit the ligament, we expected much worse when we saw the incident."
In the 29-year-old's absence Villas-Boas will have to call on one of his back-up keepers, Hilario or Ross Turnbull, for Saturday's Premier League game at home to West Bromwich Albion.
Villas-Boas also confirmed that midfielder John Obi Mikel was available to face West Brom, despite the difficulties surrounding his father's abduction in Nigeria.
Mikel played in last Sunday's goalless draw at Stoke City, 48 hours after his father, Michael Obi, was kidnapped.
"As you know it is a very, very difficult situation," said Villas-Boas. "He of course made himself available for the [Stoke] game and we are counting on him, if we decide he will play."
Chelsea will have their new teenage striker Romelu Lukaku available for the first time for Saturday's match.
"The papers are all clear," Villas-Boas said of the Belgian international, signed from Anderlecht.
Chelsea's Brazil defender David Luiz will again be missing on Saturday but he is back in training and will be fit for the visit of Norwich City the following weekend, he added.
