Van Persie was substituted at half-time during Tuesday's Nissan Stadium friendly while Welbeck pulled up after challenging for a through ball.
With Wayne Rooney back in England recovering from a hamstring injury, United boss David Moyes is hoping the pair's injuries are only minor.
"We've got a couple of wee worries," said Moyes. "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."
Rio Ferdinand and Michael Carrick didn't feature against Yokohama, but Chris Smalling and Ashley Young were both sprung from the bench during the second half.
"With Rio, we just decided to give him a rest," said Moyes. "I wanted to get Jonny Evans and Chris Smalling a game so we rested Rio.
"Michael just felt his groin. It's a bit tight from last night. It's not anything we can see keeping him out. He just missed training and the game tonight."
Moyes also said that Rooney should play some part in their pre-season campaign, while reiterating that the unsettled star is not for sale.
He said: "As far as we know, Wayne is coming on. He's started light jogging and the feedback I'm getting from the physios is that he's progressing. Hopefully those dates are still on track."