The defender missed United's 1-0 victory over Spurs earlier today and Jones' injury blow was announced via their official Twitter account after the match.
The club tweeted: "Phil Jones, who was not involved in today's matchday squad, has mild thrombosis and will be out for a minimum of three weeks."
The 23-year-old will miss games against Aston Villa, Club Brugge, Newcastle, Swansea and possibly Liverpool.
Thrombosis is the formation of clotting of the blood in a part of the circulatory system.
In Jones' absence, United kept a clean sheet and Chris Smalling was named man of the match.
Daley Blind filled in for Jones in the heart of United's defence alongside debutant Matteo Darmian and Luke Shaw.
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