The 33-year-old flanker was forced out of England’s 23-19 win over Wales on Saturday due to an ongoing knee ligament problem.
Despite limping off the field Johnson is hopeful the flanker will be in contention to play in his World Cup squad.
"The bad news would be that he has got an eight week injury that would put him out of the World Cup,” said Johnson. “I don't think it is going to put him out of the tournament, but we'll see.
"It is not great that he has got an injury, but I don't think it is on the very bad side of knee injuries."
The Bath player, who has only played five games since his injury in January, is expected to miss England’s return fixture against Wales.
"The guys like him, who have played a lot of rugby over the last 10 or 15 years, can handle that better than guys who are fairly new to it," Johnson added.
"In an ideal world he is fit and available to play the next two [World Cup warm-up] games but we will have to see how it goes."
The England boss will finalise the 30-man World Cup squad on August 22.