The 24-year-old returned from a 14-month lay-off due to the same issue in December, making a one-minute cameo off the bench against Pep Guardiola's Manchester City.
Norrington-Davies started his maiden match of the campaign as Chris Wilder's Blades eased past League Two Gillingham in an FA Cup third-round clash on January 6.
The Wales international has made just two starts in the Premier League this term for the Blades, one of which being the 5-0 thrashing at Bramall Lane at the hands of Unai Emery's Champions League-chasing Aston Villa.
The second arrived at the home of fellow strugglers Luton Town on February 10, when Norrington-Davies operated at left wing-back in a game which his side would go on to win 3-1.
However, the full-back was forced off with an injury five minutes into the clash against Rob Edwards's Hatters, being replaced by Max Lowe in the backline.
It has now been revealed by Sheffield United boss Wilder that Norrington-Davies will miss the rest of the season after picking up another hamstring injury.
The 13-time international will be unavailable for Wales' Euro 2024 playoff against Finland at the Cardiff City Stadium on March 21, when Rob Page's men will be striving to book their spot in this summer's tournament.
With the festival of European football kicking off in Germany in the middle of June, it is unclear whether Norrington-Davies would be fit in time to feature for his country at the competition.
Suffering a serious hamstring injury at the beginning of the 2022-23 term, the defender missed the opportunity to represent Wales at the 2022 World Cup in Qatar.
Norrington-Davies also sat on the sidelines as his club side raced to automatic promotion in the Championship last season under Paul Heckingbottom, finishing second behind Vincent Kompany's Burnley.
With the left-back's current terms at Bramall Lane expiring at the conclusion of the campaign, he may well have already played his last match for the Blades.
Following Luke Thomas's return to parent club Leicester City in January, Wilder only has one fit left-sided defender at his disposal in the form of Troyes loanee Yasser Larouci.