The Japan playmaker has picked up a sickness bug and was ill immediately after Wednesday night's 1-0 home defeat by Everton.
"Shinji has a sickness bug," said Moyes.
"We need to see how he is on Saturday but he wasn't too good after the game."
With Wayne Rooney suspended, Moyes could do with Kagawa being available as Robin van Persie has been missing for a fortnight with groin and toe problems.
And the United boss refused to say whether the Dutchman could feature against Alan Pardew's men.
"You can ask, that doesn't mean I will answer," he said.
"Like every club we have a few injuries. Some have a chance and some don't."
Everton's first victory at Old Trafford since 1992 has led to a storm of criticism being unleashed on Moyes, who attempted to brush it off as he spoke at the Aon Training Complex.
"It's football isn't it?" he said.
"It can happen at any club and it has happened here.
"I hoped it wouldn't but it has.
"It was our first defeat in 13 games. Now I hope we can do something very similar in the coming games."
Moyes insisted the situation was not as bad as has been depicted.
Neither did he feel the performance on Wednesday warranted the kind of training ground reaction some had suggested was required.
"I think I saw a response in the game. We weren't that bad that I felt we needed a big response," said Moyes.
"People who watched the game - they would have got lots of belief from it.
"There were chances in the game we didn't take. It could quite easily have been very different.
"Unless you are someone who doesn't understand the game too much you would have seen that.
"These are good players. They have been here before. They know what is expected of them. They will do the right things."
Moyes insisted United would do "everything we possibly can" to haul back leaders Arsenal, who have opened up a 12-point lead on the Old Trafford outfit.
There is a widespread expectation new faces will arrive during next month's transfer window, something Moyes confirmed.
"The club has always thought about strengthening," he said.
"You do that every transfer window. We will try and make that happen."