Having previously faced criticism for not finding the net regularly enough, Welbeck has scored three times in as many appearances after being pushed further forward in the absence of the injured Robin van Persie.
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"It's only a kick to his knee," Moyes told United's official website.
"He'd had a knee problem a few weeks ago, but this was a kick to it. He's trained and we hope that he's ok.
"I think Danny's a really good player, and I want him to become a really good goalscorer.
"He's got three in his last three games, so that's a good record for him and he has to try to keep that level up."
Welbeck has five Premier League goals in 11 appearances this term, a vast improvement on the one goal he managed in the 2012-13 season.