Footballer: Jones will be fit for World Cup - Giggs
Jones, 22, suffered the injury in United's 3-1 win over Hull in midweek and there were concerns that he had suffered a dislocation and would not be fit to go to Brazil.
England manager Roy Hodgson is set to name a provisional 30-man squad on Monday and Giggs says that Jones and Wayne Rooney, who has missed the last two games with a groin problem, will be available.
Giggs, who is in charge of United for the final time against Southampton on Sunday, said: "Phil's injury isn't as bad as I thought on the night.
"He's obviously out for Sunday but should be ok for the World Cup.
"Wayne has just started training over the last couple of days. Sunday probably will be a little bit too quick for him but he'll train and be fine for the World Cup also."
Holland coach Louis van Gaal is the odds-on favourite to be David Moyes' permanent replacement, with reports suggesting an appointment will be made next week.
Giggs, whose future at United remains unclear, has been in charge for the final four matches of the season and says the spell has whetted his appetite to work as a manager.
But the 40-year-old admits the whole club is looking forward to the appointment going through.
He added: "Everyone is (looking forward to an announcement). It's been a difficult season for us and when the management situation gets sorted out then we can move on and that will probably be in the next couple of weeks.
- Taste for pressure -
"There's not really a lot of pressure on me at the moment. It was four games and we couldn't really win anything, could only qualify for the Europa League and we'll carry on trying to do that.
"You get a little taste of the pressure you're put under regarding picking teams and wanting to do your best, so you get a little taste of it."
While Giggs has not been considered for the permanent role, he admits that his brief stint in charge has made him even more determined to be a manager when his playing days are over.
He added: "It just depends what time of day you're asking that question. Sometimes you probably think 'I can do without it' and other times it gives you so much pleasure.
"After the game on Saturday (a 1-0 defeat to Sunderland) you'd do without it but you learn more from defeats and not doing so well, just like when you're a player.
"But I've enjoyed it, I've enjoyed the whole experience and it's definitely helped me prepare for what will come after my playing career.
Giggs has backed proposals, which have come from a Football Association commission, for a new division in the Football League to include Premier League 'B' sides.
The plans have caused controversy but Giggs feels that it will help players to progress.
He said: "I would support it. Only speaking from my experience I remember playing at Old Trafford for the reserves when I was maybe 15 or 16 against Everton at 2 on a Saturday afternoon.
"I was playing against men and it helped me, physically and mentally it brought me on.
"I can only speak from my own experience and it definitely helped me."