The opener's marathon 138, where he batted for over nine hours, helped the Proteas draw the first Test at Lord's.
But in the final stages of his lengthy innings on Monday the 32-year-old was batting with a runner because of a groin strain.
J-P Duminy, already in the squad, is on standby to replace McKenzie when the second match of the four-Test series starts at Headingley on Friday should the injury prove more serious than first thought.
"There is a concern about Neil McKenzie," Arthur told reporters at Headingley.
"It's nothing serious. It's just with the turnaround so quick you don't have too much time to work with."
Arthur added: "I'm optimistic - I think he'll play. He had some ultrasound this morning and is going to do some strength and muscle activation this afternoon.
"He'll bat tomorrow (Thursday) and will do some training again tomorrow afternoon - and we'll put him through a fitness test on Friday morning.
"We won't leave any stone unturned in his fitness.
"If he doesn't play, J-P will just slot in at the top of the order - and AB (de Villiers) will stay at No 6.
"Anything else would be two swaps for one, and I don't want to make two changes for one position. It will just be a straight swop."
McKenzie, after nearly four years out of the side, has become a key figure for South Africa in recent times with three of his five Test hundreds all coming this year.