Kagawa started United's 1-0 defeat to Everton in mid-week, but looked sluggish and was withdrawn after an hour.
Reports suggested the Japanese playmaker had complained of feeling unwell.
Kagawa was not involved at all in the squad to face Newcastle, and Moyes told the press after the game:
"All of the stats that we look at were low so we felt we had better not take a risk in case we got an injury by playing him.
"It was a bad sickness. He thinks he ate too much, and he had to get his stomach pumped, but I think he is okay."