Jones was forced from the field with a shoulder injury 22 minutes into Tuesday's 3-1 win over Hull City at Old Trafford, while Rooney missed the game altogether with a hamstring problem.
With little more than a month until England's FIFA World Cup campaign begins in Brazil, Giggs assured fans that the duo should have no problems in being available for Roy Hodgson's squad.
"Phil's injury isn't as bad as I thought on the night," he said.
"He is obviously out for Sunday (against Southampton) but should be okay for the World Cup.
"Wayne has just started training over the last couple of days, and Sunday is probably a little bit too quick for him.
"But he is training and will also be fine for the World Cup."
United visit Southampton on Sunday, and, depending on Tottenham's result against Aston Villa, victory could see them qualify for the UEFA Europa League.
