The Blades youngster, who came off the bench during United’s defeat to Middlesbrough last midweek, was missing entirely from the squad that lost to Bournemouth at the weekend.
Tom Lockyer of Luton has also pulled out of Robert Page’s squad for the qualifiers, with Swansea’s Ben Cabango called up. Cardiff’s former Rotherham United man Will Vaulks joins him after initially being omitted from Page’s squad.
Cabango, 21, has been capped three times by Wales having made his senior debut last September while Vaulks has six caps and spoke earlier this year about his disappointment at been omitted from the squad.
Wales will face the Czechs in Prague on Friday before heading to Tallinn to take on Estonia next Monday.
They are without Gareth Bale, who has a hamstring injury, but Aaron Ramsey is back in the squad while Huddersfield winger Sorba Thomas was called up for the first time last week.
These two matches could be crucial to Wales' hopes of qualifying, with former Blades defender Page's side sitting in third place in Group E, level on points with the Czech Republic.
Norrington-Davies started the season as the Blades’ first-choice left-back, with Enda Stevens recovering from hernia surgery, and the Republic of Ireland man recently admitted that the shirt was the youngster’s to lose. Stevens played 90 minutes at Bournemouth in Norrington-Davies’s absence, giving away a controversial penalty in a 2-1 defeat for the Blades.