Vaughan, who will disclose the nature of a series of "niggles" later this week, was seen to flex his knee occasionally during a fine innings of 72 on Tuesday in Yorkshire's eight-wicket County Championship Division One defeat against Durham at Headingley.
Instead of taking the field for the final session after tea, Vaughan had ice pack treatment on his knee.
Moxon said: "It is difficult for me to say too much, but Michael has a few aches and pains which he will speak about at the press conference later this week.
"His knee is a little bit sore. But there is no danger of him missing the Test match, and he will explain things more fully on Friday."
The first Test between England and South Africa is at Lord's from July 10 to 14, with the second match at Leeds from July 18 to 22.