Manchester City striker Tevez caused a stir when he carried the bag for his Argentinian compatriot Andres Romero on Sunday at Royal Lytham.
Golf fan Tevez, a 13-handicapper, admitted he could not give Romero any advice but enjoyed the experience nonetheless.
The move has drawn criticism from McArthur though, with the R&A committee chairman saying the issue needs to be looked into.
"He never put the bag down, even when he was standing on the green - it's just absolute madness," McArthur was quoted as saying by several papers.
"I think we need to to look at this particular case. We normally get a list of caddies at the start of the week."
R&A chief executive Peter Dawson took a different view of the incident, saying: "It was pretty interesting. I thought, because of the big crowd following the group, that golf fans and football fans may overlap a little more than I had realised. It's not a bad thing, perhaps."
Tevez was at Royal Lytham on Saturday to watch Romero, who started the Open with rounds of 70 and 69, shoot 77.
Tevez then took the bag for Romero's final round, which saw the 31-year-old card an 82 to finish last in the tournament of the players who made Friday's cut on an 18-over total of 298.