Anderson, who took seven wickets in the victory, is to undergo scans on a side injury after struggling through the fifth-day at Newlands on Tuesday.
"He's been such a great servant that we're holding our breath and have fingers crossed for him," Ashley Giles, director of England men's cricket, told BBC Radio 5Live.
"We'll be desperate if Jim was injured again. He's worked so hard to get back in the team.
"We certainly don't think it's a recurrence of his previous injury."
The third Test of the four-match series, which is level at 1-1, starts on January 16 in Port Elizabeth.
The 37-year-old spent time off the field in the afternoon session at Newlands, but did bowl a two-over spell after tea. He finished with figures of 2-23 from 18 overs.
Despite clearly being in some pain he remained on the field and took catch at leg slip off Stuart Broad to remove Rassie van der Dussen.
Anderson has just returned from a five-month lay-off with a calf problem.
England captain Joe Root said: "He'll go for a scan, get some treatment and we'll see how he pulls up going into the next Test in Port Elizabeth," said Root.
"It's his side, but it could be just a little niggle. It could be a 24 to 48-hour thing or it could be something else.
"Until we have more information we'll just treat it as best we can and fingers crossed he's not another casualty of this tour."
Opener Rory Burns flew home after injuring his left ankle playing football on the eve of the game and has now been ruled out for four months.
However, England are hopeful pace bowler Jofra Archer, who missed the second Test with a sore elbow, will be fit for the third Test.