Van Persie - who was the Premier League's leading scorer in his first campaign at Old Trafford in 2012-13 - was taken off at half-time with a thigh problem, while England international Welbeck pulled up sharply with a groin issue but continued.
These injuries compounded United's misery as they were beaten 3-2 at the Nissan Stadium on Tuesday, meaning new boss Moyes has now seen his side lose two of their three pre-season friendlies to date.
Moyes is already without the unsettled Wayne Rooney, who had to fly home just a few hours after arriving on the tour with a hamstring injury and is being heavily linked with a move to Chelsea.
"We've got a couple of wee worries," the manager told MUTV. "Robin just felt his thigh in the first half and we didn't want to take any chances.
"Danny Welbeck felt his groin when he came on and we've just got to make sure they're all okay especially with so many games coming up.
"We've still got a few games to play before the season starts when we get back home."
Moyes will hope his side can bounce back to claim a win over Cerezo Osaka in their next pre-season game on Friday.