Benteke suffered the problem at Norwich on Saturday but, speaking after Tuesday night's 4-0 Capital One Cup defeat to Tottenham, Lambert acknowledged the damage was not as extensive as he originally thought.
"It is not as bad as we feared it was going to be," said Lambert.
"Maybe four, five, six weeks or so."
Lambert confirmed Benteke would not be fit for his country's World Cup qualifiers next month.
Indeed, if the player is out for a full six weeks, he will not be available until the beginning of November.
"The medical people give you the best and worst-case scenario," added Lambert.
"You are never quite sure until you hear from the professor.
"Thankfully it is not too serious.
"It has got a lot better and he is feeling a lot better, and the international break certainly helps us."
Source: PA
Source: PA