Shaw, a £27million capture from Southampton in June, is set to miss United's Barclays Premier Legaue opener against Swansea on Saturday - as well as further league fixtures against Sunderland and Burnley - due to the injury.
The 19-year-old left-back made his Red Devils debut in a 7-0 friendly win over LA Galaxy last month but will not be able to make his league bow for his new club this weekend, which will also mark boss Louis van Gaal's first competitive match at the helm.
A statement on Manchester United's official website read: "Luke Shaw has suffered a hamstring injury and will miss the opening game of the season against Swansea City on Saturday.
"The England international, a summer signing from Southampton, is likely to be sidelined for around four weeks.
"Shaw sat out the friendly victory against Valencia at Old Trafford due to the problem and faces a wait before making his competitive debut for the club."
News of Shaw's setback came shortly after United announced their squad numbers for the 2014/15 Barclays Premier League season.
As expected, Shaw inherited the number three jersey from Patrice Evra, who joined Juventus in the summer, while Adnan Januzaj was handed the number 11 shirt previously occupied by Ryan Giggs, who has retired from football to become Van Gaal's assistant manager.
Ander Herrera, the midfielder signed this summer from Athletic Bilbao, has taken number 21 in place of Angelo Henriquez, who has departed to Dinamo Zagreb on loan.
Juan Mata has been given number eight, with fellow midfielder Anderson being demoted to 28.
No-one has claimed the number five or 15 shirts worn previously by Rio Ferdinand and Nemanja Vidic, the centre-backs now with QPR and Inter Milan respectively.
United confirmed on Twitter that any further new arrivals will be handed vacant shirt numbers, which could include reported target Marcos Rojo.
The Sporting Lisbon defender is being hit with disciplinary action by his club amid talk of him being wanted by Van Gaal.
Reports suggest United have made a bid of around £16million for the 24-year-old Argentina international and that Rojo has refused to train with Sporting, handed in a transfer request and asked to be allowed to join the Red Devils.
Sporting president Bruno de Carvalho has been quoted as saying that both Rojo and team-mate Islam Slimani are "subject to strong disciplinary measures" and will not play in the club's Portuguese league opener against Academica on Saturday.
De Carvalho, quoted by Portuguese newspaper Record from an interview with Sporting TV, said: "They will not play next weekend
This will take as long as it takes
If something doesn't change, you're going to end up with the players seeing out their contracts."
He added: "These two, in defence of our magnificent group, must be removed
They are subject to strong disciplinary measures.
"Both players have taken decisions that have caused sharp indiscipline at Sporting."
Source : PA
Source: PA