Manager Louis van Gaal moved to play down fears by claiming the substitution had been a “precautionary measure”.
“It does not seem to be too serious, but we did not want to take any risks,” Van Gaal told Dutch broadbaster SBS6.
Van Persie, 29, has scored four goals in three matches since joining United from Arsenal in a £24m deal last month.
Van Persie also scored in the Netherlands’ 2-0 World Cup qualifying victory against Turkey on Friday.
Shinji Kagawa is another injury worry for United having missed Japan’s World Cup qualifying victory over Iraq with a back injury.
“I felt a twinge in the back during practice when I was on the ball. I had some treatment but didn’t want to risk causing the team trouble by playing,” Kagawa told the Kyodo news agency.
“Obviously it’s a shame I wasn’t able to play. It’s not that serious and I don’t think it will keep me out for long.”
United play Wigan Athletic at Old Trafford in the Premier League on Saturday.